As @HDawg23 said above, not even close. I have career time trial (or cup) times for all three cars recorded on my spreadsheet from Suzuka GP (not similar in any way to Lime Rock Park but a good reference):
P1: 1:28.3
F1 GTR: 1:33.0 (+4.7s)
Regular F1: 1:35.5 (+7.2s)
The F1 GTR will likely be good for D at best, maybe C. It's hard to tell right now since Lime Rock Park's short distance can throw some spanners into the mix.
P1 and its not close, as HDawg and Lambo said. Top speed is its only disadvantage, but it’s not a substantial difference. Braking is effectively the same between the two when FU, but the P1 has a gargantuan acceleration and handling advantage. Lime Rock’s a track where handling is vital and this is the South Circuit, which has quite a few sharper corners, so the P1’s superior handling will let it carry more speed through them and superior acceleration will let it pull out quicker, so this should be an easy win for it
