You need a definite article in front of "kis". He is a specific, definite László. But it is still hard to explain why. Without the adjective ("kis") you would not need the article. With the adjective, you do.
I came here fully expecting the comments below and I didn't fall foul of the rule. There is a very similar question involving A kis Éva and from memory I think she was stepping from the bed to the table but I'm not sure. There is consistency here!