I dont know anyone who has built a replica LHIRES III from scratch but Ken Harrison’s L200 which was also available as a kit initially and then was briefly offered commercially has a lot in common with the LHIRES design.
The history of the LHIRES is an interesting one and explains why the full details are available.
It came out of a pro-am conference in France where the usefulness of amateur measurements of Be stars was discussed. A spectrograph with higher resolution than was currently available to amateurs would be needed though. An amateur team (Including Christian Buil, Francois Cochard, Olivier Thizy and many others) got together to design one and in 2006 arranged for the manufacture of a kit of parts on a not for profit basis though the Aude amateur astronomy group. They expected to make perhaps a dozen but got orders for over 70 ! (I have kit #29). Requests for the kit kept coming in after the first batch so Francois Cochard and Olivier Thizy formed Shelyak Instruments to make it commercially and the rest as they say is history.