With Edit> Find & Replace we can search: [a-z], tick "Match case" & "Regular expressions" then find all to select cells containing lowercase letters.
SEARCH function supports regular expressions but does not use Tools> Options> Calc> Calculate> Case sensitive.
So SEARCH function does not distinguish between upper and lower case letters.
It is therefore impossible to do the same search as above:
As workaround we have to do =NOT(EXACT(UPPER(A2);A2))
Steps to Reproduce:
1. Open FindLowerCase.ods attached
2. See B3 result is 1
3. Tick or Untick "Tools> Options> Calc> Calculate> Case sensitive" according to the status of the option
4. See B3 result
#VALUE (no lowercase in A3)
User Profile Reset: No
All functions (e.g. COUNTIF) that support regexp should also use this option.
Created attachment 159900 [details]
The case-insensitive behaviour of SEARCH is defined in the OpenFormula . Additionally, starting with v.7.0, regular expressions in functions honor (?-i)/(?i) flags  (tdf#78840). So =SEARCH("(?i)[a-z]";A2) should work in v.7.0.
Closing WONTFIX, do you agree?
(In reply to Mike Kaganski from comment #2)
> Additionally, starting with v.7.0, regular expressions in functions honor
> (?-i)/(?i) flags  (tdf#78840).
Blimey, I had searched (badly then). Thanks a lot, you and Eike, of course.
> Closing WONTFIX, do you agree?
of course :)