Call Lakeside Yacht Club, they may have room there. Also, they have an agreement with the neighbor Repo lot (Sailing Inc.). You can store your truck and trailer there, for a small fee, and it's secure... it's a boat repo lot.

I used to store my trailer there all summer long... anytime access included.
Lakeside - 216-432-3270
Sailing Inc - 216-361-7245
Hey... one more thing... if you see a Penguin walking the streets... maybe looking a little hungry... toss him a ten spot. He's a good Penguin, just hit some hard times.