I probably don’t have a real solution for you, but for the record, images uploading on Buddypress will not have a same CSS everytime. Just think about it, because avatars and cover images are new images uploading into our database, and lazy load will exclude core images (which have specific classes throughout). If you’re planning to add the uploading image area into lazy load, it will probably not work also since you’re using the class of the surrounding/background/border/area not the actual image that is uploaded.
Second of all, I have the same issue as yours. And my solution is to officially turn off lazy load. Because lazy load can actually affect our SEO rather than helping it grow. And the resolve is too hard to figure out since it’s not the problem of both theme and Buddypress, neither will have a solution (And lazy load plugins are one time development, noone will stick around to adjust this upload that for us).