There are several challenges to mounting the coils to the keg lids. The first is that the lids have to be tilted on an angle to be inserted into the lid opening. There is trigonometry involved. The overall length of your coil is limited by the diameter of the keg and the angle of inserting the lid and it isn't going to be anywhere near long enough. My plan was to limit the amount of tubing that was actually coiled/folded back on itself and allow for that portion to be raised and lowered so that the required lid angle could be achieved. Unfortunately, I decided not to do the math and I eyeballed all of this, which is why I messed on on the fold back version. On the coiled version, I was able to compress the coils further than shown below and cut off the extra length. The lids are a bit clumsy to get it, as they only if you tilt it at the correct angle and rotate it into place. It gets easier the more times you do it, but no where as simple as those triclamp fittings on the top of conicals. The arrows I drew on the keg help.
Next problem to solve was how to mount the coils so that they can be raised and lowered. A simple rubber #2 stopper would be easy, but I want to be able to ferment under pressure. I decided to use compression fittings and BobbyM/brewhardware.com had welding spud compression fittings. I decided to solder these onto keg lids, but even that presented some problems. There is not a lot of real-estate on every lid. I had to find one that either had no PRV or that the PRV was not centered. Also, the latch needed to be wide enough to clear the tubes. Luckily, I found a few that would work. I also needed to make a racetrack version for one of the 10gal kegs. I thought that would be easy because my lid did not have a PRV, but it was a little more problematic because those lids are slightly domed and I needed the spuds to line up in parallel. A block of wood and a hammer got me close enough.
I'm currently using small o-rings in the compression fittings. Once I decide if it is better for the coils to be 1/2", 1", 2", etc. off the keg floor, I'll switch over to the permanent, SS ferrules.
I use a brass compression/NPT fittings and a brass barbs to connect the hoses. For simplicity and cost, I had wanted to use push connect fittings, but they could not latch onto the SS tubing. I later learned you could score the tubing with your pipe cutter and give them something to grab.