How long does the drowsiness take to where off when taking 0.5mg lorazepam?

Hi, Caz!
Two days in is still very early for side effects to resolve... usually it takes just days to a week or so.
Your metabolism needs to adjust to the medication being in your system and that's why you're feeling drowsy.
It's great that it's helping to control your anxiety symptoms!
Be sure to take it exactly as directed as it can become habituating quickly if you take more than prescribed and it's generally recommended that it be used not longer than six weeks. Have you tried more long term medications like the antidepressant/anxiolytics such as Lexapro, Zoloft, Paxil, etc.?
Best regards and I'm happy that you're feeling better.

The half life (meaning how long half the amount of the drug is still in your body) of lorazepam is 12 hours. It takes approximately five half lives for a medication to be eliminated from your body. So 5x12 = 72 hours. If you’re taking this medication daily the drowsiness may continue.