The English cognate is 'lich' and yes, it is the same word as 'like'. It originally meant 'form, shape' - thus a 'lich' is something in the form of a human, but so too forms most of our grammar: so + like = slik/such (swylc), who + like = hvilken/which (hwylc, and æ + ge + hwylc in Old English = æghwylc > each). Thus is gas the meaning 'a form in this way' or 'which form?'.
As I've asked in another thread (the "all animals are equal"), how do I know that the sentence uses "lik/like" as "alike" and not as "equal"? Especially here, since "i'm like you" ("we both have similar personalities" ie.) it means something very different from "I'm equal to you" ("i don't have privileges" i.e.)