Does this park, or any nearby, have a place where my dog can swim? She could remain leashed if I could wade in.

Not at this park...You may want to ask Google search for place where my dog can swim near me...

Hi Alyson, short answer, no. You want to try Rosie's Dog Beach in Long Beach or Sepulveda Basin Off-Leash Dog Park in Van Nuys.

It's a beautiful place, but the lake is dirty

There is small man made Lake but I wouldn't recommend it for swimming.