I have two files - both large, about 120,000 words long.  One is the manuscript for my novel, which LO edits in quite a snappy fashion (let's call this MS).  The other is basically the same, but with a very large number of comments from a professional editor (let's call this MS-ed): LO clearly has some kind of O(N^2) algorithm (or worse) when it comes to handling comments, since it struggles horribly to edit this file.  (Both are in .odt format.)  Maybe LO is using a linked list structure to hold all the comments? :-(

The number of comments is not something which is reported in the Document Properties->Statistics, so I have to estimate the number.  There are 339 pages, so I roughly estimate somewhere between 1000 and 3000 comments.

If I hover over the drop-down arrow on a comment, the balloon text appears quite promptly. If I then click on the arrow to pull up the context menu for the comment, I have to wait about 12-17 secs for the menu to appear. If I choose to delete the comment, that operation takes between 10-15 secs to complete.

My workaround is to break the document with comments ("MS-ed") into two halves, and work on each half independently.  By halving the document, the time to pull up the Comment context menu drops to about 1 sec, as does the time for the Delete Comment operation to complete.

Some of the comments are lengthy, BTW (e.g. 100 words).  Average comment text length is maybe 20 words.

This is on an Intel NUC (AMD x64) with 16GB RAM.
Ubuntu 14.04.

Hope this information is helpful.