I know you probably get inundated with tons of replies and that's probably a pain to deal with, and you might never ever even see this comment, but I've put some thought into this so I figured I might as well try just throwing the idea out there.
What I'm thinking is to change it so that if the Lifeline is knocked while a DOC res is still in progress, the res gets cancelled. It's a simple change, but it would make it so that it would be more viable to push against a knock on a team with a Lifeline (who is still up) cause you wouldn't need to divide your attention between the res and the rest of the team. As long as you're able to successfully focus down the Lifeline on your push, the res is no longer a concern. It still remains a powerful and useful ability, the change just slightly nudges the needle to give a bit more of an advantage to a team pushing a knock/res against a Lifeline.
I hope you might at least give some consideration to the idea, and thank you ...
I don't think it would solve the frustration case where Lifeline plays around the doc drone res shield and you can never knock her. I think by the time you've knocked Lifeline, you've won that fight anyway, so cancelling the res at that point is gilding the lily.