After Bryce Dejean-Jones' jumper put the Rebels up 72-71 with 12 seconds to go in the extra period, Lyons potential go-ahead basket from just right of the free throw line bounced out with 3 seconds left.
Lyons, the Mountain West Conference scoring leader who finished with 19 points, didn't think he rushed the shot.
"I don't think it was too soon. It just didn't go in," he said. "If we had won, I would have considered it a steal. We need to rebound better. We need to finish out games."
UNLV's Khem Birch got the rebound, was fouled, and hit two free throws with 1 second left. After the Falcons (9-5, 1-1) turned the ball over, Dejean-Jones was fouled and hit two more free throws.
"We wanted this to be our statement game," said Falcons forward Mike Fitzgerald, who had 22 points. "We wanted to come in and beat a team in the top tier of our conference just to prove we can beat anybody. Nothing went wrong (at the end of overtime). They had a couple of good shots and we missed some."
Fitzgerald believes the Falcons' narrow loss "just proves we can play with anyone. We just wanted to get some respect out of this game — to show we can challenge anyone in this league."
The Falcons, who kept it close throughout the game, trailed by eight at halftime before pulling to 54-52 on Lyons' layup with 7:55 left in regulation. Kyle Green's 3-pointer then put them ahead 55-54 with 5:42 remaining.
The Rebels tied the score at 58-all with 3:37 left on Justin Hawkins' 3, and the game went back-and-forth until Dejean-Jones — who scored 16 of his 18 points after halftime — hit two free throws to tie it at 62 with 36 seconds left in regulation.
Fitzgerald had a chance to win the game for the Falcons in regulation but missed a 3 with 3 seconds left, sending the game to overtime.
Mike Moser had 14 points and 11 rebounds for the Rebels. DeLovell Earls added 10 points for the Falcons.
The Falcons took the lead with 3 minutes left in the extra period and didn't trail until Dejean-Jones made his go-ahead basket. Lyons gave Air Force its last lead at 71-70, making 1 of 2 free throws with 39 seconds left.
Air Force has had little success against UNLV in Las Vegas as the Rebels improved to 19-1 against the Falcons at home, including 17-1 at the Thomas & Mack Center. Air Force's only win came in 2006.
UNLV, which led 38-30 at halftime, shot 50 percent from the field in the first half, but 32 percent in the second half and had a seven-minute stretch with no field goals. The Rebels also were 6 of 25 (24 percent) from 3-point range.
The Rebels also had 23 assists, with Anthony Marshall getting 12.
Air Force Falcons guard Todd Fletcher (10) dribbles the ball up court as UNLV Runnin' Rebels guard Bryce Dejean-Jones (13) defends in overtime at the Thomas and Mack Center. UNLV defeated Air Force 76-71 in overtime.