LZEXE is a utility that compresses an executable file into a smaller, self-extracting form. It was used in most early id and Apogee games, and many others. LZEXE compressed executables can be unpacked by a few different utilities, the most widely used being UNLZEXE.
An LZEXE compressed executable can be recognized by the presence of the tag "LZ" at offset 0x1C in the .EXE file, followed by a version number that is either "09" or "91". Such executables must be decompressed before any useful inspection or hacking of the .EXE can take place.
Note that some programs change the LZ91 signature to disguise the fact that LZEXE has been used. If there are four sensible-looking characters at the same offset there's a good chance the file has been compressed with LZEXE and had its signature changed. Luckily most decompression utilities don't look at this so they can decompress the file anyway.