How are they competing?
I'm not sure but I think it means that delta spreads more efficiently, so delta infects many of the vulnerable in the vicinity. When a lambda tries to infect someone, there's a high probability that delta has been there already and left that person with some immunity, so lambda has more trouble finding a victim to keep its chain going, and dies out.
ETA: I think I'm saying the same thing as PG. Not sure what you mean re:natural immunity.