If l- tyrosine is taken at night can it keep awake or cause insomnia ?

Possibly: I don't believe there is much research on this, but l-tyrosine can be converted to the neurotransmitters Dopamine & norepinephrine which are stimulating. It may also result in lower serotonin levels (important for sleep). I always advise my patients who take it to take it in the morning or early afternoon. If you took it and can't sleep this should pass within a few hours. Try some exercise!