score:4
10:27am to 11:54am is insanely tight. The domestic to international MCT at JFK is 1:15 so I think the booking is possible but JFK is notorious for issuing impossible MCTs (at one point United was selling a ticket with a transfer time of 30 minutes to a different terminal!). So you are a full 12 minutes above the official unrealistic MCT. Nope.
You land at LGA at 8:10AM, let's say you clear that airport in 40 minutes, that's 8:50AM, the drive over should not be more than 40 minutes but even if it's 60 you have two hours to go through JFK check-in and security. This is way more realistic.