Through Batavia it's still an active rail line. And there is still some active track immediately east of P&L Jct.
There's a section which is a trail near Buffalo and most of what's in Monroe County is a trail, through Rochester Jct., although at I-390 there is no underpass, you have to go around. Some of the branch into Rochester is also a trail.
Phelps Jct. is well east of Rochester, but it's worth noting that a number of bridges have been removed at various locations in addition to the property being private - both those the LV used to pass over other lines and waterways and those that crossed over the LV. Just east of Batavia, for instance, a large bridge was removed and a ramp built to connect the remaining track to the NYC (or Erie) branch that crossed under. And the time I hiked the bit of LV at Rochester Jct. the ROW west of the former crossing appeared to be impassable with some kind of fill on top of it. Bridges east of there through Caledonia have been removed.
I would plan to stick to the trails, and you might be able to get a release from GVT to hike the bit in Batavia too. It's active, but not very active. In Lancaster I noted it appeared to be passable as an ATV trail, but who knows who owns it.