Lanzante, the car's maker that is renowned for its work on customer McLaren F1s and F1 GTRs, clocked a 6min 43sec laptime at the Green Hell with its machine, which is 9sec quicker than the latest record holder, the Lamborghini Huracán Performante.
To emphasise its road worthiness, Lanzante said the car then drove off of the circuit and home to the UK.
The P1 LM is claimed to be the quickest, rarest and last of the P1 variants. Just five production models are being made.
Lanzante says the biggest change from the P1 GTR is in the engine hardware, which now produces additional boost and hybrid power to keep the full 986bhp from the P1 GTR. It also gets gold-plated heat shielding in the engine bay, and the charge coolers have been tweaked to be more efficient at higher temperatures.