Hi Joe,
As they say in the car manuals, re-assembly is the reverse of disassembly
.
I don't know your lathe at all, but on mine the procedure is to put things back together and then move the leadscrew up, down or sideways until the half nuts will close easily on it at the headstock and tailstock ends.
Up and down is dealt with by loosening the leadscrew bearing block fixing bolts at one end, clamping the half nuts up at that end, then tightening the bolts up. If the leadscrew doesn't rotate freely, the holes in the bearing blocks may need enlarging to allow a bit of wriggle room. Then repeat at the other end of the leadscrew.
Sideways adjustment can be accomplished, if there is sufficient wriggle room on the bolts which hold the apron to the saddle, by loosening them, closing the half nuts, and then tightening the bolts up again. If that doesn't work, shims behind the bearing blocks, or skimming a bit off their backs, may be necessary.
You can often diagnose what treatment is needed by closing the half nuts half way along the leadscrew, while observing closely to see if it flexes at all. If so, the leadscrew will be put under severe strain when the carriage gets near one or other (or both) of the bearing blocks.
Andy