Guys, looking up Article II, §4 of the Indiana Constitution wasn't exactly hard:
No person shall be deemed to have lost his residence in the State, by reason of his absence, either on business of this State or of the United States.
IC-3-8-1-1 sets the qualification for candidacy at no more than being a registered voter in the election district (in the case of the Senate, that would amount to merely being registered in Indiana). IC-3-5-5-18 expressly allows for residents of "nontraditional residences" to register.
So state law says that he keeps his registration when he's in DC, he's qualified to run by virtue of being a registered voter, and he may remain registered even if his residence is deemed to be his hotel instead of his family farm (which, incidentally, another provision of state law addresses). I'm not saying it would be impossible to make a case to kick Lugar off the ballot, but I am saying that it would be a better use of his opponents' time to just campaign against him and let the voters do their thing.