Hi Again,
With regards Button 17 in Post #3 (1st Page)
17. monogram letters L.C., silver plated 17 mm, no backmark .
I think it maybe for 'Lowther College".
Having searched on-line, I am assuming it is this Girls College -
https://en.wikipedia.org/wiki/Lowther_College
I found this (see picture below) in a Book called "Scholastic Arms " by G.K. Beaulah published 1936.
There looks to have been quite a few late additions to the book as it says '
Prints added to this collection subsequently are not described among the blazons' - and this is unfortunately, one such late addition.
However, when I have looked on line, this is not the crest of the school - as that is a 'very busy/intricate' design - see here:
https://amounderness.co.uk/lowther_college,_lytham.html
Of course, for a relatively small college, it may have been easier/cheaper to go for the fairly simple "LC" design on buttons instead of trying to replicate the school's crest.
Btns - I hope you don't mind, I have copied your original button into this post to make it easier to compare the two side by side.
All the best
Ian