That is a good question. Are there any requirements for residency in that state to run for office? If not, anyone could run there.
The other question I have is whether Lugar pays taxes in that state since he doesn’t have a legit address there?
U.S. Constitution, Art. I, section 3, cl. 3: a U.S. Senator must, "when elected, be an Inhabitant of that State for which he shall be chosen."
If Lugar voted in Indiana, then it appears he also committed a fraud.