Lara had another daughter?

I don't know.

Yes, at least in the movie. Yuri and Tonya are shown on a balcony waving as the army passes by; she is holding a baby. The scene shifts to the country where Pavel is leaving Lara to join the army. She is holding a baby. Yuri's brother narrating the scene says something to the effect that men in happy marriages do not leave their families to join the army. The child with Lara and Yuri at Varykino must be that daughter. Her name is Katya. When Lara leaves Varykino with Katya, that is the last we see of her. I don't know if that is indicated in the book as I haven't read it.
Lara names her daughter with Yuri, Tonya, like Yuri's wife. Again, I haven't read the book, but I saw a comment that said that Lara and Tonya had met, Lara having assisted at the birth of one of Tonya's children, and that they liked each other. The letter that Yuri receives from Tonya at Varykino informing him that she and the family are being deported and that she has given birth to their son also acknowledges Lara, whom she opines is a good person, and acknowledgement that she knows that Lara and Yuri are together. She has visited Lara before she had to leave Varykino and left the balalaika with her.
Lara names her child with Yuri for Tonya, an acknowledgement that only the circumstances of separation from each spouse have resulted in them being together, their love for each other notwithstanding. Lara never forgets that she and Yuri are married to other people.