One of my bandmates and I are using two different layouts ( he is using the standard Big Lyrics - Portrait layout, I copied that layout and tweaked it a bit for me). We are using the same type/size device (Amazon Fire tablet 10). However, whenever one of us resizes and saves the text size on a song, it saves it for both of us. Is there any way to keep the text size specific to a layout or user?
Yes, one or both of you can turn on Settings > Account Sync > Personal Sync > Lyrics Font Sizes and then your size changes won't affect the other one.
Ideally you'd have a sense of which of you is using a "default" font size, and then the other person would turn on the personal sync. That would ideally be used for the less typical settings. For example, if one person has reduced vision and needs the text to be uncommonly large, that would be the best person to turn on personal syncing.