I did an unscientific poll. Ten out of 10 native Frankfortonians I interviewed did not know the name of the lake for which Lakeview Park is named after.
If no name exists for the lake, perhaps it could be named "Parkview Lake" or "Lake Pond." (Depending on your definition of a lake.) One gentleman I spoke to about the lake said, "I thought it was called 'No Fishing Lake,' because I saw it on a sign there."
Regardless, this controversy needs to be settled should Lakeview Park become the nexus of Franklin County tourism its boosters claim it will become. Perhaps the absence of a lake at Lakeview Park will be the quirky draw for out-of-county visitors, justifying the added expenditure at the park while so much of downtown Frankfort sits idle.