Are heat lamps are designed to reheat food when food falls under 135 degrees?

That statement is False.

most of them are designed to reheat food when it falls under 165 degrees

hope this helps

No. The heat lamps are not designed to reheat food when food falls under 135 degrees.

Explanation:

A heat lamp is an incandescent light bulb that is used for the principal purpose of creating heat. Heat lamps aren't counseled for holding doubtless venturous foods hot at a minimum of one hundred thirty-five degrees Fahrenheit. 
In order to heat up a doubtless venturous food for decent holding the food ought to be cooked-over quickly to a minimum internal temperature of a hundred and sixty-five degrees.