Although relatively unknown, Lindsey Graham had every right to run for president, as do any of the candidates. Until exposed to public opinion and media scrutiny, it is highly difficult to predict any outcome in an election, especially one of such high office. In running for president, Graham had the ability to increase his visibility and influence public opinion in doing so. Just because he was unsuccessful does not mean he could not have been successful.
Yes, Lindsey Graham should have run for president. He thought he would be good at it, wanted to be president and had supporters. He was right to run. Anyone who wants to run for President should. Perhaps some people should keep their expectations low, but that is not the case with Graham. It's unfortunate he got out as early as he did.
No, in my opinion Lindsey Graham's campaign was doomed from the start. Graham joined an election join an primary with far too many contenders and had little in the way of policy or political capital to differentiate himself with the other Republican candidates. Voters have shown in this election that they want radical change which Lindsey Graham failed to offer.
Even if I supported his party, his profile isn't high enough to get enough support. He doesn't really have a chance to win the nomination, so he'd basically be diluting the pool of possible candidates anyway. Plus he seems to have more influence on his party working from behind the scenes.