There wasn't "one" Laker, as it were.
When Laker started across the Atlantic, it was not possible to make advance reservations (at which point BA, Pan Am and TWA introduced "standby" fares). Prospective passengers simply queued and took their chances. However, it evolved quite quickly into something else, with "APEX" (Advance Purchase Excursion) fares and a "premium" offering, for example.
Laker grew into a sizeable operation. I remember being quite impressed by the large number of departures Laker had from LAX to the UK whilst I was waiting to board BA's (lone) departure to London one day in August, 1981.