There is't much of a difference between the two sentences. The only distinction would be surrounding the subject matter. For example, if I were to say "Give me a hand with putting this puzzle together" that would make perfect sense. But If I said "Lend me a hand with putting this puzzle together" that would sound odd. So basically, if you're saying "Give me a hand" then you usually associate the phrase with a physical task. "Lend me a hand" would be more of a phrase that stands alone. Like if you were having money troubles and asked a friend for help, you might say "I'd appreciate it if you would lend me a hand".

Adding a wrinkle with respect to usage, we also say "give him/them a hand" to mean give the person/people an applause, at least in the U.S. So it's entirely possible that some smart-aleck will clap (applaud) you if you say "give me a hand".