I'm not sure that the lilies are choking out the almond or not. If you can dig them out without damaging the tree's roots you can do it as an experiment. More than likely the almond has another problem that is causing the dieback. Not knowing your location, the recent weather, and seeing it for myself, all I can provide is a guess.
You'll notice, if you read other posts in this forum, several of us frequently recommend talking to your county extension agent. He or she should be able to help you free of charge.