New cat - 6 yrs old very timid

My childhood cat that I've had since I was 8 passed recently and we we're very close. She was very vocal and would carry on a conversation with you forever. She also laid on my lap in my computer chair and lay by me at night. 

I now have a new kitty and I want to make sure that she is adjusting well. 

She is a 6 yr old 7lb (we think Chantilly) cat

She was found with feline lice, treated, and was at the shelter for 6 months before we adopted her. She was adopted out once but then returned for being too shy. 

She has no front teeth but eats food just fine

At first she was hiding underneath our couch and in the closets but now she sits on the cat trees and in her cat cubbies. 

I can see she's starting to gain her confidence and is walking around on her own and will come out from hiding spot when called and no longer has to be coaxed out. 

She has never hissed or bitten us and is always very sweet.

She loves to be picked up and held over the sholder (like burping a baby) she purrs and kneeds everything whenever petted.

However she never meows and does not like to lay down on my lap or near me.

I'll be holding her and petting her (I let her down immediately if she wants me to put her down) and then if i try to place her on my lap, she jumps down. 

She spends a lot of her time in the cat tree. We have another younger cat (2yrs old 12lbs) and they will touch noses for about 5 seconds, the younger cat hisses and then they walk away. They never swat at each other and lay a foot or so away from each other with no issues. 

Will it take time for her to warm up to laying near me? Is just feeling scared or threatened in the new home? Or is it probably just a personality thing?

Since she is shyer, it will take her some more time to warm up and for you to discover what her personality quirks are. Not all cats are talkative, so she may not ever be like your old cat in that way, but she will have her own personality and habits that are unique to her. She is spending most of her time in the cat tree right now because she does feel safe there. You can encourage her to feel comfortable around you with treats and toys if she likes to play a lot. You both are still figuring each other out right now, but she may never like laps like your other cat. For example, my cat will never sit in your lap, and she doesn't like to be held either, but if you lay down near her she loves to come over and rub all over you and then climb up on your stomach for petting. It's just the way she prefers to do things!