When does the burning from Lexapro go away?

Hi, Britt!
As masso mentions, these are common to very common side effects when starting an antidepressant/anxiolytic. The burning sensation is called parasthesia and it and the insomnia should be resolving quickly now for you.
Consult with your doctor who can give you advice and also to your pharmacist. They can make recommendations for remedies that can help, some are even OTC.
Best regards, Wildcat
"Psychiatric
Very common (10% or more of users): Insomnia (up to 14%)"
"Nervous System
Common (1% to 10% of users): Dizziness, lethargy, paresthesia, tremor"

I took Lexapro (Escitalopram) for a year, it was a of great help for me, it is a good antidepressant.
I had only sexual side effects and I discontinued the use of this antidepressant because these side effects which for me, lasted the entire year. I didn't experience any other side effects as everyone reacts differently to medications.

Having said that, very common to common potential side effects do tend to affect some users, up to 10% give or take at the beginning of the treatment and tend to subside within a week to 10 days in most patients if they don't subside you must contact your Dr./Psychiatrist.

Less common side effects:
"burning, crawling, itching, numbness, prickling, "pins and needles", or tingling feelings"

Very common:
Insomnia up to 14% of users

I advice you to contact your Dr. and discuss the burning sensation, as I mentioned it is considered a less common side effect. With regards to the insomnia, also mention it to your Dr. perhaps he/she can prescribe a sleep aid to deal with it while it subsides.