There is a parking lot in Downtown Lakewood on HWY 32 across the street from Subway. Plenty big for trailers. I actually think it has trailer stalls. There is no road running needed to get to the trail, its right there from the parking lot.
Yep good parking areas up along Hy. 32/Nicolet State Trail....If you are coming from the south ,which most are, there is parking available in Mountain also which is about 5 miles south a Lakewood.
If you want overnight parking head up 32 to the casino in Carter. They have a huge well lit parking area with gas across the street and the trail runs right next to the parking. I don't recall how far from Lakewood but its before Laona.