Marcus Jackson's 3-pointer with 3:18 left in regulation gave Rice a 64-63 lead, but the Owls went scoreless the rest of the way. De Lattibeaudiere made the first of two free throws with 1:59 left to knot the game at 64.
Lamar's last-second heave was no good at the buzzer.
Rice only made two field goals in overtime, both 3-pointers, the last pulling the Owls within 75-72 with 55 seconds left. Lamar made 4 of 6 free throws in the final minute.
Jackson and Max Guercy scored 19 points apiece for Rice (3-7).