Careful BroJos. The "drawing of lots" from the USATF rulebook looks to be written only in cases where there's another round to run (prelims to semis, semis to final, etc.). This tie was in a final and, obviously, there's no further round, since this is the U.S. National Champs meet. I'd argue that it should stay a tie. That does leave the problem about who runs in London. If the tie was for 1&2, or 2&3, there'd be no problem.
The USATF rulebook looks like it didn't plan for a third place tie. Four names (three plus an alternate) get named by the national federation to the Olympic team, so any decisions don't have to be made quickly. There won't be a run-off during the Trials.