See http://cleveland.citysearch.com/listing ... 67948_4288
I've never used any of these, but when I searched for tourist apartments near Cleveland I found nothing.
We often rent an apartment when we are overseas, but tourist destinations usually have a network of tourist apartments, which can be rented by the week or even day. I guess Lakewood, or even Cleveland, is not a tourist destination.
There are also home exchange programs, and sometimes one of the homes can be rented, rather than exchanged, but I don't know of any here.
It would be nice if you could find someone who will be out of town in August. We probably won't, but I'd often be happy to have a house sitter when we are gone.