I did the job myself over the weekend. Parts from Ford came to $313 and I had to add transmission fluid when finished so a few extra dollars for that plus a fluid pump to add the fluid. I did all four lines that go with the transmission cooling system, I figured it was worth the extra $130 dollars or so than just doing the steel lines and I didn’t have the tool to disconnect the quick connect fittings. I contacted a local shop and they quoted me $1340 to do the job and to do the transmission flush and fill recommended at the service interval. My truck has a little over 100,000 miles on it. Transmission service was $350 of that quote. If you decide to buy the parts the dealership will need to know the VIN number, so there must be a couple different versions made.
Pretty straight forward job if you have experience working on cars but running the lines is a pain in the butt and it was messy. If you decide to do it, I found that removing the wires to the starter helps give you more room.
Transmission fluid runs through these lines so I don’t think a coolant leak would be directly related to this exact issue. I am not a mechanic so I can’t say that with 100% certainty though. I had transmission fluid running down the cooling line on the input (drivers) side and dripping off the bottom, that’s how I noticed the problem.
I didn’t mean for the original post to seem as much as a crisis as the linked video seems, but just to give people a heads up and to be aware of a potential problem and to check their truck.