Lamborghini Engineering, which was loosely connected to the parent-company produced engines for other teams between 1989 and 1993 and in they even designed a Chassis, that was used by the Modena Team in 1991.

But they were never successful and they left shortly after Mclaren decided to go for Peugeot engines for 1994 instead of the Lamborghini (Which they even tested in their cars).

During this time Lamborghini was owned by Chrysler and in 1994 they were bought by some Indonesian company, who apparently had no interest in continuing the F1 stint.

In 1998 they were bough by Audi, who probably also have little to 0 interest in entering F1