Checked with:
LO 3.5.4.2 
Build ID: own W7 debug build
Windows 7 Professional SP1 64 bit

Could not reproduce. Applied Numbering in two separate actions - numbering restarted in second list.

Additional comment:
I used Line numbering - Restart at this paragraph - Start with 1 option.

Created attachment 63868 [details]
shows the problem of the ordered lists

The attached document shows the problem. I created a new blank document,
then clicked on Numbering in the Styles and Formatting window to create
the first item of the first list. Pressing Enter, I created the second
item. Then I created a paragraph "bla bla bla" with default formatting
and then again an ordered list with Numbering. Note that the first
item of the second list starts at "3".
But I want it instead to be numbered at "1". To do it, I must apply
a local change to paragraph formatting (Numbering, restart).
This, instead, should be embedded into the Numbering style, much the
same as what the <ol> html tag does.

Created attachment 71650 [details]
Document with numbering ok

I think you can workaround this by using special numbering and styles.

Here a sample.
perhaps there are other methods...

Created attachment 89471 [details]
ODT and PDF showing the 3 ordered list entry methods from Writer Guide v4.0.

I am confirming this bug under Ubuntu 10.04 running v4.1.3.2 Build ID: 70feb7d99726f064edab4605a8ab840c50ec57a. Status set to NEW. There is a problem with the manner in which ordered list numbering is handled with respect to the use of styles (paragraph and list), as originally reported:

> Paragraph styles for numbered lists do not have a means to specify
> that the numbering be restarted.

This is correct. Only direct formatting (Format > Paragraph...) can be used to restart list numbering in styles. First a few corrections:

(In response to comment #2)
> I used Line numbering - Restart at this paragraph - Start with 1 option.

Line numbering is a separate facility to list numbering, regardless of the method used to number a list. The indicated settings have no effect on list numbering (nor should they).

(In response to comment #5)
> I think you can workaround this by using special numbering and styles.

Broadly speaking, yes, it is possible to workaround the issue as described e.g., by direct formatting. The sample provided in comment #5 however uses outline numbering via the Tools > Outline Numbering facility and sets different levels for the first and subsequent items (even though they are the same level). This is a hack.

There are three different methods of defining ordered lists and in the attachment I have indicated where these are described in the Writer Guide v4.0. The first two use direct formatting and work. The last one, of which I provide two examples, uses only paragraph and list styles, and exhibits the problem as reported. 

I will test these three methods under older versions of Writer if I get the chance over the coming days, to determine whether the behaviour as described has always been this way (likely), or is a regression (less likely).

The problem is still present in release 4.4.
Someone suggested that it can be solved by defining a paragraph style
for the first item in a list and another for the following ones.
I think that this is a hack. The real solution is to have a paragraph
style that means: "list", and a paragraph style that mean: "item", much
the same as the html <ol> and <li>.
The current solution of having numbered paragraph styles allows to have
only one list in an entire document only, and to mimic several lists by
manually forcing restart numbering the first item.

(In reply to Angelo Borsotti from comment #8)
> The problem is still present in release 4.4.
> Someone suggested that it can be solved by defining a paragraph style
> for the first item in a list and another for the following ones.

That's the way it is documented for a long time. Before suggesting new features, try to make the existing features usable (as the original reporter did).

> I think that this is a hack. The real solution is to have a paragraph
> style that means: "list", and a paragraph style that mean: "item", much
> the same as the html <ol> and <li>.

Paragraph styles are not SGML. I see no need to define complex container structures like items consisting of lists, or empty lists, etc.

> The current solution of having numbered paragraph styles allows to have
> only one list in an entire document only, and to mimic several lists by
> manually forcing restart numbering the first item.

If the proposed fix were implemented, lists (at the top level at least) would work OK. Probably instead of unconditionally resetting the list numbering, the list numbering at the current nesting level should be reset.

The problem is still present in LO 4.4.5.

The LibreOffice Writer Guide incorrectly says that exactly this feature exists in both LO 4.0 and LO 4.2 (i.e. that "Paragraph styles for numbered lists ... have a means to specify that the numbering be restarted.").

The Guide even shows screen shots of a Paragraph style window open at the "Outline and Numbering" tab showing a "Numbering: Restart at this paragraph" checkbox and "Start with" field:

Figure 205 on page 199 of LibreOffice 4.2 Writer Guide
https://wiki.documentfoundation.org/images/e/e6/WG42-WriterGuideLO.pdf

Figure 199 on page 187 of LibreOffice 4.0 Writer Guide
https://wiki.documentfoundation.org/images/3/35/WG40-WriterGuideLO.pdf

This checkbox and field are absent in my copies of LO 4.0.6.2 and LO 4.3.5.2 running on MacOS 10.5 and 10.6 (although there's a suspicious gap in that window under LO 4.0 where I suspect that checkbox used to be).

I downloaded the oldest LibreOffice version available (LO 3.3), and confirmed that this checkbox is absent there as well; hence this problem seems to have been inherited from OOo.

So this is not, in fact, a new feature request, but a feature that was once present (in OOo?), and is still documented in the LO Writer Guide.

Still present in LibreOffice_5.2.5_Win_x86.msi.

I can confirm the bug still occurs exactly as originally described. I am using:

LibreOffice Version: 5.3.0.3
OS: Ubuntu 14.04LTS 32 bit

Can confirm this on 5.3.1.2.

Even checking the option to restart numbering on this paragraph, the numbering will not restart when the style is applied to another paragraph. 

The expected behavior is that when the option is checked the numbering should restart when the style is applied again to other paragraph in the document.

I have verified that the problem is still present in Release 6.0.

I also confirm this exists.

Very frustrating to not have a style that will restart numbering.

I prefer style because it can follow another style without having to click on the numbering button.

Reproduced in:

Version: 7.3.0.0.alpha0+ / LibreOffice Community
Build ID: cd2b5168e8ef1cb6e721bc5220421464ed723096
CPU threads: 8; OS: Linux 4.15; UI render: default; VCL: gtk3
Locale: en-AU (en_AU.UTF-8); UI: en-US
TinderBox: Linux-rpm_deb-x86_64@86-TDF, Branch:master, Time: 2021-07-21_14:56:23
Calc: threaded

and:

Version: 7.2.0.1 / LibreOffice Community
Build ID: 32efc3b7f3a71cfa6a7fa3f6c208333df48656cc
CPU threads: 8; OS: Linux 4.15; UI render: default; VCL: gtk3
Locale: en-AU (en_AU.UTF-8); UI: en-US
Calc: threaded

Steps followed:

1. New Writer document
2. In Styles sidebar, apply List style > Numbering 123
3. Add a couple of list items
4. Press Enter twice to then create a non-list paragraph (e.g. Text body)
5. Add another line and apply the Numbering 123 style again.

Result: the numbering follows the last item in the previous list.

With cursor in the first item of the second list, "Format > Paragraph > Outline & List > Restart numbering at this paragraph" does work to have it restart at 1.

However, "Style > Edit style... > Outline & List > Restart at this paragraph" does not have any effect. But it's hard to even know what "this paragraph" means, given that it's supposed to apply to the whole style... (Note that this edits the Paragraph style, not the List style.)

In my opinion, as we have List styles, there should be an extra option in the list style options dialogue to restart the numbering when the items are not contiguous. But I might be misunderstanding the role of list styles.