The LS904 output their analog sin waves:
product.heidenhain.de/JPBC/image/HWP.DE/...06-92_ls_804_904.pdf
You will need EXE's to do the A/D conversion before inputting the signal to the Mesa. Whether you use a three axis EXE board like the one you mentioned or three individual ones is only a packaging issue. On my Maho, I had a similar three axis EXE. One channel was dead, and one was unreliable. I now use the one functioning channel, and two stand alone EXE's.
Those three axis EXE boards are three completely separate channels. There is no electrical connection between them, Not even the supply power or ground are common.