Is it really necessary to have letterhead for recommendation letter from employer to apply for US universities?
Letters of recommendation should be in business letter format, which contains all the information of letterhead.  Letterhead, while it makes a letter look more official, is usually not necessary (in fact, for some applications, you just type the "letter" into a text box on a website).  (Occasionally applications will specify something like the letters should be on department/university letterhead, which presumes the recommender is an academic.)  A former dean of admissions at Chicago Law school concurs.

For sending printed letters, letterhead does provide a layer of authenticity, but if you can't use it, then you can't use it.  However, nowadays, most letters are sent electronically, with the writer's email address or the like providing the requisite authentication.  I don't usually bother with letterhead for e-letters unless it's specifically required.