When in doubt, read the t&c of the policy (which is more liberal than DOT requires). The 24 hours starts when the tickets are purchased, not when the reservations are made. The e-tickets, presuming that LH confirms, will be time-stamped.

if, of course, has to be this way in OP's situation as LH has 72 hours in which to accept or reject the reservation, thus permitting UA to confirm the ticket. Until this occurs, OP has a reservation, but no ticket.

This, of course, presumes that OP is booking through .com or UA's phone system.