Indiana has a sore loser law.
Which means once a candidate loses a party's primary, he can't then file to run for office as an independent in that year's general election. He would have to withdraw from the race today, before the polls open tomorrow unless is is already to late to withdraw from the primary. If Lugar loses tomorrow, he won't be on the ballot in November.
Texas has a similar law. In fact Texas law makes it quite difficult to get on the ballot as an independent. Not only can the person petitioning not have been a candidate for any position in a party primary, but the people signing the petition must be registered voters who did not vote in any party primary in that election cycle. There is not only a requirement for total statewide signatures, but there is also a requirement for minimum numbers of signatures in each state senatorial district, and there is a pretty short time during which signatures can be collected.
I am assuming then that the lawsuits to overturn it will take place on Wednesday?