It depends on how you define the word “lying”.
According to Wikipedia-
“A lie (also called prevarication, falsehood) is a type of deception in the form of an untruthful statement, especially with the intention to deceive others.
To lie is to state something with disregard to the truth with the intention that people will accept the statement as truth.”
When you lip-synch in shul are you intending to deceive others?
Are you lip-synching so they will think you are singing or are you doing it for yourself?
Are you doing it with the intention that other people will accept it as the truth, in this case really singing?
I say no. If you are standing next to someone and you are lip-synching, they know you aren’t really singing. Would you try to make them think you are singing? No. You aren’t doing it with the intention that others will think you are actually singing. Do you really care if people know you aren’t singing? From your post, I get that you are doing it for yourself, to feel more involved.