We do a lot of similar things.
A few more...
We haven't started the timer yet but I'm starting to teach Penny the word "turn." eg If I'm sharing an apple with her, I hand it to her and say "Penny's turn" and when I take a bite, I say "Mama's turn!"
A phrase I use is "play too." So if Lydia has out all her princess dolls, she can hand one to Penny and let her play too. Or she can go to her room and play. I'm not going to keep the baby out of one of her elaborate princess party setups in the middle of the living room floor.
I encourage her to get Penny her own book to look at or to find another stuffed animal to play with, as examples, so that Penny can feel included.
Lydia can always yell "help" if they aren't getting a long.