The most common way would be to take Rt 28 south from Old Forge, merge on to Rt 12 south into Utica, and eventually Binghamton. 28 and 12 are a nice drive - 2-lanes most of the way with maybe 10 or 15 miles of 4-lane just north of Utica. From Binghamton you can pick up I-81 into PA and down to Scranton (just noticed that "Old Forge" is a Scranton suburb...funny). Never actually been to Lancaster, though, so beyond Scranton, I have no suggestions.
From Scranton I would be inclined to take I-476 south to I-78 west to PA-61 south to US-222 south to Lancaster. There are no ideal routes, only the lesser of several "evils". Be sure to stop at Cabela's at the intersection of I-78 and PA-61.
I would not take I-476 the whole way south to I-76. There is major construction for the last 10 miles of I-476, with narrow lanes and aggressive drivers.
You could also take I-81 south to Harrisburg, picking up I-83 south and then PA-283 to Lancaster. Do this only if you hit Harisburg at midday. I-83 on the east side of Harrisburg is congested and not RV friendly. If you choose to go this way, stay in the left lane of I-83 at all cost. By the time you see the left exit to PA-283, you will have no time to move over if you are in the right lane.
The easiest way out of central NY to PA is via I-81, and it's a pretty drive as well as interstate-efficient. You can pick up I81 at Syracuse, about 30 miles west of Rome. Rt 12 is a decent alternate as well - have done them both.
From the junction of I81 and I78, you can get on PA 72 to Lancaster. It's an adequate road but not a great one. If you prefer the 4 lane divided highways, stay on I81 to I83 and then take I83 and 283 into Lancaster. I83 gets city-type traffic at rush hours, but it's not a terror.
Would you stop in Hershey, PA, on the way? The "Town that Chocolate Built" is a fun stop too.
Just a FYI their is a roalroad bridge on the south side of Old Forge that will be listed in the trucking Atlas as a low bridge. It was its no longer low, no they did not raise the bridge the lowered the road.