It sounds like a really good start. You are fortunate that Lilo is such an accommodating kitty. That is going to make things much much easier initially. Sheri is right though that what you did was a bit reckless. Sometimes kittens do come home with life-threatening and contagious illnesses, in which case you risk losing both cats. And it seems to be really common for the kitten to have some parasites initially as well. At least make sure the kitten gets looked over by the vet this first week, ok? That should happen regardless.
I did the same when I got my second cat, with the same result you had in terms of the two cats getting along. My resident cat was just off-the-charts accommodating of other cats, and everybody or everything that walked in the door was instantly her best friend. It actually made *me* jealous sometimes... nothing like your cat deciding that your new visitor is their best friend at first sight, lol. She took one look at the kitten I had gotten from the shelter, and proceeded to wash her from head to tail. The kitten was soaking wet afterwards, I actually had to towel her off
It's a cat's way of saying "you belong here now, let's get that other smell off you and make you smell like you belong".
As far as the play goes... you'll have a learning curve in understanding what is really going on. It sure sounds like Lilo is just very gently playing with the kitten. When the kitten gets older, it is going to be harder and harder to tell. Generally you want to take your cues from the kitten. If the play is making the kitten upset to the point where he is cowering or hiding or whatnot, then it is probably going too far. If he bounces back afterwards, and wants another go at it, even if it looked (and sounded) too rough, then it is probably ok. Definitely err on the side of caution initially, but usually pet parents tend to read more aggression into the "rough play" than is really there.