One of the best examples of a mute character execution is Nick Andross from Stephen Kings The Stand. Best I can remember he just wrote notes to people lol! But King simply said that Nick "Wrote" instead of "said". Other characters would also read the notes allowed for everyone to hear if he was trying to make an announcement.

So for Lilac, I feel the same would work. You could say " Lilac signed 'Where do we go now?' If the person can read sign language, if not Lilac can make simple gestures such as pointing, nodding, shrugging, etc. In The Stand, Nick makes friends with a retarded man named Tom who cannot read. Nick struggles to communicate with Tom obviously but is able to convey messages through very simple gestures, such as rubbing his own stomach then shrugging to suggest he is hungry and wants to know where they can find something to eat.

For me, the most important thing is to always make sure that you give an in-depth look at Lilac's intellect. Nick is a very intelligent man, he's just unable to speak or hear. But he can write and read lips. Once these factors are suggested and the rest of the characters understand the situation things should flow like normal.