There are 2 families of widebody trijet invented in 1970's after the invention of Boeing B747, the first widebody aircraft in the world, Douglas DC-10 & Lockheed L-1011.
The L-1011 was the most advanced aircraft in 1970's, which is the first aircraft in the world featuring fly-by-wire system, earlier than Airbus A320. It is also installed with Rolls Royce RB211-22 engine, the 1st engine having more advanced 3-shaft design for lower fuel comsumption & noise (Rolls Royce BR211 & Trent are still the only 3-shaft engines now). But its capacity is quite small & its range is very short, just 5500km, much less than the competitior DC-10's 10000km. These factors & its lateness in production mainly due to Rolls Royce engine late delivery makes very few L-1011 produced, only about 200. Lockheed, however, projects production of 500, so this leads Lockheed's withdrawal from commercial aviation market.
The DC-10, however, is very successful despite of much less advanced technologies, because of higher capacity & longer range. The DC-10, however, had a lot of problems, so Douglas decided to launch MD11 of improved design & longer body in 1986. It is again very successful until the arrival of A330, A340 & B777 because it was the only aircraft lying in the 250-350 seating range.
Even so, there are quite many airlines, like British Airways, Air Canada, Cathay Pacific, choose L-1011 instead of DC10 / MD11 just because of Rolls Royce engine on L-1011, which is not found on DC10 & MD11. What happens if there is Rolls Royce engine option for DC10 / MD11 or if there is no Rolls Royce engine option for L-1011? There would be even fewer orders for L-1011.