Hello there!
The first thing to know about aggression is that is elevated fear. So, Lexie needs a reeducation to learn not to be afraid. Try and see Scout from Lexie's perspective and how big a Border Collie must seem to a Yorkie.
You must rethink all of your interactions with Lexie including playtime, which is now becoming a problem. If you were Lexie's size and you wouldn't want it done to you, don't do it to her. Praise her with treats when she is calm and obedient. Practice simple commands like sit and reward with treats to build confidence.
Are you giving her enough exercise? My 7 month old Yorkie needs the same amount of exercise as my older and bigger Cavalier King Charles Spaniel. I have also realized my Yorkie is much quicker to learn and needs a lot more intellectual stimulation then my Cavalier. She learns tricks in one day and then we just reinforce them every day. If we don't she gets bored and then, destructive or angry. This is the difficulty of smart dogs!
I think its great you are going to an obedience class. Obedience classes will give you the tools to help Lexie be calm and well behaved and not bite. Just remember what you put in is what you will get out of it. Just going to the classes is not enough.
I just read Victoria Stillwell's book "Its Me or the Dog," and I found it to be more useful for both my dogs and me then any of the other training books I ever tried. Its simple and clear and gives living guidelines to reinforce for a happy pup and owner. I just posted on the topic today, actually!
Check it out here:
Its Me or the Dog! | CupOFdog | Dog Site for Dog People
Hope that helps and things are going better!