We received this solution from someone who didn't give their name:
Lachlan is $3$
David is $7$
C is $12$
I first looked at the ones with Cassandra in and found the difference, which was $4$, so that means David and Lachlan's ages have a difference of $4$. I then worked out that $7$ and $3$ have a difference of $4$ and make $10$. So, either David is $7$ and Lachlan is $3$ or the other way round.
When I took $7$ from $19$ to get Cassandra's age, that made $12$ and it also made $12$ if I took $3$ from $15$, so it must be that way round.