Hey, welcome to the boards, although I don't know if I should be the one to say since I just joined less than an hour ago!
But anyway, I think you're expected to do a bit more extensive research on LSQ and its properties, and compare them to what you already know about ASL. Umm excuse me for rambling on, but I'm going to do just that. At least I warned you, in all fairness.
I guess the main thing and most obvious aspect about LSQ is that it's used by francophones so it probably still maintains most of the properties of French Sign Language. But take note that ASL was also derived from French Sign Language although it's changed extesively since its derivation. Comparing ASL and FLQ would be like comparing English and French, although I suspect that a variety of the signs in FLQ are the same as ones in ASL. Grammar would be a huge difference, though. For example, in French, if you wanted to say "Look at the red car," you would say, "regardez le camion rouge." The adjective comes after the noun there, and the verb ("regardez" or "look") is a command but has a different form for each different tense.
Something to take note of, though, is that a lot of signs in ASL use one of the letters to define them. For example if you wanted to sign "Library" you'd use an L-shaped hand, whereas in French, "bibliotheque" means "library" but this time it starts with a B so you can't really do that, can you! These are only really small details, off the top of my head, that I didn't arrive at through any kind of research - just common sense. So I wouldn't take my word for it without doing some research of your own.