Lugar is standard "reasonable conservative", but with Republican party marching further and further to the right - that's not enough anymore. Barry Goldwater and Ronald Reagan would lose present day Republican primary as well... The same with Jimmy Carter and. possibly, Bill Clinton in Democratic primary by similar reasons..
Er, not sure what you're getting at. Carter was and is well to the left of Obama. When Obama was running against Hillary in the '08 primary, it was frequently noted that 95% of their policy positions were the same. Hillary might be very slightly to the left of Bill, but I doubt it. Either way, Bill Clinton's views are still very much within the Democratic party's mainstream.
Not sure. Both parties (Republican to the greater extent, but Democratic too, at least - somewhat) are more and more dominated by "activists", for whom you can't be "conservative enough" in Republican case and, correspondingly, "liberal enough" in Democratic. Carter was an "old style populist", so he may be to the left of Obama on economy, buy not sure about all "hot" social issues - he was born ad raised in rural Georgia, and may be too "traditional" for these "activists"