Is it normal for anxiety to increase when upping the dosage of lexapro (escitalopram)? If so, how long could that last?

Yes. This is a common reaction and the duration should not be too long (perhaps a few weeks at most - hopefully less) but each person is different. If otherwise you are pleased w/ the effects, try to bear it. If it's too bad or too long - ask for alternatives. Don't just stop! Work closely during this stage and consider adding CBT therapy to optimize the benefits!