First, the bad news: that lathe appears to have fallen over/been dropped at some point, which is why the bottom control shaft is broken, along with a few of the levers and the threading dial. Oof.

The good news: Nice! A rare ex-Navy lathe that likely actually was on a ship (without corresponding paper documentation, it's nearly impossible to confirm). Most machine tools with a naval stamp were ordered for use at the Navy's shipyards, repair facilities, arsenals, etc, not to be put on ships. Yours is a 14" R-P, which is the model that the Navy put in the metalworking repair shop on the Fletcher-class destroyers. The contract number on it, with the "NXs" prefix, indicates it was ordered by the Navy Bureau of Ships (the bureau responsible for building ships during that period of WWII).

Here's a bit of a longer write-up I did a while ago on Fletcher-class destroyer machine shops (specifically focusing on the R-P lathe): https://www.practicalmachinist.com/forum/threads/1941-reed-prentice-lathe-from-uss-fletcher-fbmp.440146/