correct wiring of a preamplifier and a lock-in amplifier
I'm assuming you need to supply +20V (5), -20V (4) and power ground (3) seperately.

I'd wire the preamp to the lock-in amp with a BNC lead from the lock-in amp to pin 1 and 2 on the pre-amp and check that you get the desired performance. 

Have the lock-in amp working differentially if you think performance isn't good enough.

Then, if all else fails, I'd contact the supplier and ask them what they'd recommend - they are the experts.

Do this before you think about building a box for the simple reason - until you have a benchmark performance you are happy with, you cannot tell if when introducing a "neater" box will deteriorate the signal in any way.