It might help if you better specify the parameters your using:
I.e.
- Have you applied any upgrades?
- Have you tried any tunes?
- Have you adjusted the top speed on the transmission?
- What tyres are you using (game version as well)?
- Are you driving legally (keeping to track limits)?
- Are you having trouble with the handling, tyre wear or just general lap times?
This race is not necessarily difficult, and certainly shouldn't be an issue in an LMP unless you dislike driving them. If you don't like the handling of the LMP try a different car - a Mazda Furai, Team Oreca Viper, Maclaren F1 etc... are all plenty quick enough to win.
Otherwise, you could try deliberately starting with a wet race, based on experience it is much easier in the wet, and offline, the Racing Wet tyre is never the fastest tyre around this track, whatever the conditions (based on experience).