The formal answer to your question is "Yes. LoadRunner can be installed and run on Linux."
Please, see the list of supported Unix-system for two latest LoadRunner releases (v8 & v9):
For LoadRunner 9.0:
Solaris (Solaris 2.9 and 2.10)
HP (HP-UX 11.i V2)
IBM (AIX 5.2 and 5.3)
Linux (RedHat Linux Advanced Server 3.0)
For LoadRunner 8.0:
Solaris (Solaris 2.8 or higher)
HP (HP 11.x or higher)
IBM (AIX 4.3.3 or higher)
Linux (RedHat 9.0 or higher)
If you asked about "pure" Linux, LoadRuner can be run on RedHat only.
Also, pay attention that *NIX platform can be used as a Load Generator in a LoadRunner load-testing scenario.
LoadRunner Controller, Virtual User Generator and Analysis tool are only supported on Windows-based machines.
If you are not familiar with these terms, I will explain in simple words:
LoadRunner on Lunix can execute only tests, not create, edit, start or analyze them.