Torph debuted in the World Rally Championship during the 1980 season, entering the Swedish Rally and the 1000 Lakes Rally in Finland in a Volvo 142, retiring in both events. Progress came slowly, but his seventh WRC start at the 1984 Swedish Rally produced his first championship points — a fifth-place finish in an Opel Ascona for Opel Team Sweden. In 1985 he placed eleventh at the Swedish Rally and added more points at the 1000 Lakes Rally with a ninth-place finish in a Volkswagen Golf GTI for the Swedish Junior Team.
The 1986 season marked Torph's breakthrough as a regular works-supported competitor. Competing in three rallies for Toyota Team Europe, Toyota's factory WRC outfit, he drove a Toyota Celica TCT to second place at both the Safari Rally and Rallye Côte d'Ivoire — endurance events on African terrain where he finished as runner-up to his own compatriot and teammate Björn Waldegård on each occasion. At the Olympus Rally he finished fourth, this time ahead of Waldegård. The points accumulated across those three events placed Torph sixth in the drivers' world championship for the year.
In 1987, again on a three-event Toyota contract, he drove to third place at the Safari Rally with a factory Toyota Supra 3.0i, completing the gruelling event despite suffering from fever for almost its entire duration. The result came behind Audi Sport's Hannu Mikkola and Walter Röhrl. That season's Rallye Côte d'Ivoire was abandoned following a tragedy unrelated to the competition: Toyota's support aircraft, a Cessna 340, crashed and exploded on the second day, killing team manager Henry Liddon, his assistant, the pilot, and the navigator. Toyota boss Ove Andersson withdrew all factory entries from the event.
The 1988 Swedish Rally produced Torph's fourth and final WRC podium — third place in a privateer Audi Coupé Quattro, behind Markku Alén and Stig Blomqvist. He also accepted a factory drive with Volkswagen at the 1988 Safari Rally but retired after his Golf GTI 16V developed an engine problem. Torph carried the Audi Coupé Quattro into the 1989 season opener at the Swedish Rally with Team VAG Sweden, but retired again due to an ignition fault.
Torph was not entered as a competitor at the 1989 Monte Carlo Rally. He had travelled to Monaco to carry out reconnaissance and help fellow Swedish driver Fredrik Skoghag develop pacenotes for icy road surfaces. Taking a break from recce duties, Torph and his regular co-driver Bertil-Rune Rehnfeldt went to watch the fifth stage of the event as spectators from the roadside.
During the stage, Italian driver Alex Fiorio lost control of his Lancia Delta Integrale, briefly regained it, and then left the road at approximately 145 km/h (90 mph), crashing down an embankment into the two Swedes. Both Torph and Rehnfeldt were killed instantly. Fiorio and his co-driver Luigi Pirollo were uninjured. Fredrik Skoghag immediately withdrew his entry from the rally. Lancia's factory Martini Lancia squad finished the event with a clean sweep of the podium: Miki Biasion first, Didier Auriol second, and Bruno Saby third.
Lars-Erik Torph's death at 28 underscored the danger that roadside spectating — and even recce work — posed at WRC events during the era, when crowd control and course access restrictions were far less stringent than they later became. His rally career, though brief, included competitive results in the sport's toughest endurance events on the Safari and Ivory Coast circuits, two second-place finishes for Toyota, and a consistent points record across nine seasons of WRC participation. He is remembered as a capable and determined privateer who earned legitimate factory opportunities, and whose life ended through no fault of his own while simply watching a sport he had dedicated himself to.