Kentucky was pro-union, especially so in the crucial city of Louisville and other areas in the Ohio valley. So it seems unlikely the Confederates could ever get a significant force into the state of Ohio, let alone to Lake Erie.
Would Kentucky be pro-south, or at least parts of it, if the Union had invaded it first?
Why would they need to invade it unless they had seceded? Your argument is circular.
Say the Confederates are holding up well and aren't being pushed back, so some Union commander gets the idea to invade from Kentucky to throw them off and finally push them back.
If Kentucky joins the CSA in 1861 could the csa assemble an army at Some point during the American civil war and cross the Ohio river and reach lake Eire in Ohio
Short of several major military disasters in rapid succession for the North in 1861 and extraordinarily good luck for the CSA, I don't see it happening.
However, there was a Confederate plan to hijack the sole USN vessel on the Great Lakes--the USS Michigan. But that would have been a purely naval effort.
Here's a blog post that I wrote on that subject a couple of years ago:
http://www.neatorama.com/2013/12/11/The-Confederate-Navys-Crazy-Plan-to-Raid-the-Great-Lakes/