I posted too soon. If I'd only looked a little closer at the page I referenced, it had a link to more specific info on the NASM's LM. It is Lunar Module 2 (LM-2) and was intended for unmanned testing. However, LM-1 on Apollo 5 was so successful that the LM-2 test was cancelled. Instead, it was fitted with landing gear and used for drop testing. LM-1 flew without landing gear because it wasn't needed in Earth orbit.

Here's a link to the 12 Lunar Modules built as flight hardware. The only two that survive intact are LM-2 at the NASM and LM-9 (built for Apollo 15 but replaced by the J-Series LM-10) at JSC.

According to this source, LM-13, intended for the cancelled Apollo 18 mission, is at the Cradle of Flight Museum in Garden City, NJ.

This source says the LM-14 vehicle (Apollo 19) is at the Franklin Institute in Philadelphia. It also says that LM-15 (Apollo 20) was scrapped.