I have never seen a shower tray supported by those little legs. I don't know if one would be avail to do that. I t looks like you also have one corner with only dirt under it. I am guessing the best (or at least easiest) way to solve you mess will again be to use the concrete. Put enough gravel in so the pipes don't become in "the mix". I have to say I am glad this is not my bath you have a real mess on your hands. May the force be with you.
The photo looks as though the remaining concrete forms an L shape, I'd get rid of it and have a smooth floor to put a new shower tray on.
Hire an SDS drill from the local hire centre, this looks like an oversized drill but importantly it will act as an electric chisel so you can easilly shift that concrete.
The lead pipes are a worry not only because once disturbed they can contaminate your water ( years of build-up in the pipe coats it and makes them safe, but bending them makes this coating come off) but to join lead pipes to copper or even plastic is highly specialised!
It's rare to find lead piping in a house, most older houses have it from the meter but has been joined to copper by some point. Lead has the disadvantage of having a small diameter hole so less flow compared to the same outer dimension sized copper or plastic. the fact you have it in your bathroom would indicate it is used throughout your home, unless this is a downstairs shower.
Anyway, in my opinion I'd get rid of the lead and convert to plastic.
You can get trays with legs but they don't last long and feel very cheap underfoot as tehy shift with your weight.
Where does your waste go? A quick option may be to fill in the hole with bricks to the height you want, leave room for the waste and place the tray on top, there would be a step tho.