If it has banjo bolts in the brakes, then it is an earlier 56 with Lockheed drum brakes. Girling disc brakes (like my current 56 has) used ordinary double flare fittings instead. As Art mentioned, one advantage of the banjo fittings is that you can easily replace the sealing elements when they become work-hardened through many R&R cycles. With SAE flare fittings, the line itself forms the seal, and has to be replaced after a fairly limited number of cycles. That's why the racers generally eliminate the flare fittings.
Sorry, no help on conversion; except you might look into whether you can buy AN adapters that will fit. Personally, I didn't like the Lockheed drum brakes on a previous 56 TR3; I never could get them to work consistently every time and they seemed much more prone to fade than the disc brakes. So if I was going to do any conversion, I'd convert to disc brakes. But YMMV of course.
Here's a good article on brake plumbing, with lots of references for more reading:
https://www.dimebank.com/tech/BrakePlumbing.html
One of the Carroll Smith books has a good section on brake plumbing as well. Unfortunately I can't recall the name at the moment, but it's the one that he wanted to call "Screw to Win".