Within his First Amendment rights? Absolutely. Is the school district's decision "to no longer include prayer at graduation" a First Amendment violation? Given the phrasing, I'd guess the district's decision passes Constitutional muster. It sounds like the district simply no longer sets aside a time for prayer in the program, not that the district is prohibiting any of the scheduled participants from conducting such activities.
(I don't provide a link for the above quotation because I'm pretty sure the article, like most of Yahoo!'s content, is highly perishable and won't be available a month from now.)
I suspect I'd be more supportive of a student who chose to highlight the tragedy of the Syrian civil war, or the ongoing discrimination against LGBTIQ youths in high schools across the country. Reflecting on my bias, I think I'm probably wrong to feel good about any of these outbursts.
I'm a big believer in propriety on such public occasions, not for its own sake but because it is a sign of respect to one's audience. They're gathered there for a purpose that has nothing to do with your political, religious, or other beliefs. You have been given the privilege of speaking, and in return they extend to you the courtesy of listening. To lecture them just because you know they're not going to deny you the courtesy they promised, violates that implicit bargain.
"But the Lord's Prayer isn't a lecture!" Oh, yes it is, certainly in this case. The student's action was clearly a protest against the district's decision.
But even if you sincerely believe that his recitation was merely a prayer, you can't argue it was a harmless act.
His prayer pushed his religious beliefs front and center, as did the audience's reaction. He and most of the audience — for all I know, it could have been all of the audience — may believe that high school graduation deserves a religious component. That doesn't make their belief right. In our pluralistic society, it is at best impolite to permit one faith a more prominent role in non-denominational ceremonies than other faiths. This was a public high school graduation, not a graduation from a private, religious institution. Any non-Christians in the audience likely felt marginalized by the recitation and the boisterous response it received. Those non-Christians didn't deserve to feel marginalized. They attended the ceremony to see a loved one graduate, not to be reminded of the overwhelmingly Christian makeup of the local population.
That's exactly the sort of coercive influence that the First Amendment was designed to prevent government from facilitating. In this case, of course, it wasn't the government taking action, it was a private citizen. That means the action was legal. But being legal doesn't make it right. Such a public display of faith during a non-denominational ceremony is simply bad manners. And just so we're clear, taking sides in the Syrian civil war or demanding equal rights for LGBTIQ youth during a graduation speech would be just as rude and inappropriate.
Students are there to graduate, not to proselytize, no matter how worthy the cause.