2-hour layover between flights, LaGuardia to JFK

TL;DR: which checked bags: no. Without checked bags, very risky.

From the information provided, we can guess that:

• your first flight is AA1608, which is scheduled to arrive at 3:02 pm at LGA, but is often delayed
• your second flight is AA1416, departing at 5:10 pm from JFK.

If you have checked baggage, the deadline for an international flight is 60 minutes prior to departure, that means 4:10 pm.

This leaves barely over an hour (if the first flight is on time) to:

• exit the plane
• make your way to baggage reclaim
• wait for your bags
• exit the airport and find the place to catch a cab
• possibly wait for one
• travel to JFK (Google says 28 to 45 minutes driving)
• find the right place to drop your bags
• queue
• drop your bags

This seems impossible to me. Even for a same-airport connection without luggage checked through this would be considered risky, but adding the travel from LGA to JFK makes it impossible.

If you don't have bags to reclaim and check, then it could be doable, though very tight (even though you don't have the 60-minute bag drop deadline, you still have to go through security and get to the gate 10 minutes before the departure time), and of course subject to delays on the incoming flight. At the very least you should get a seat at the very front of the plane, and check out terminal maps beforehand to know your way. You should of course have checked-in for your second flight online, otherwise you're back to the 60-minute deadline.

As both your flights are on the same airline, did you book them as a single ticket, or where they booked separately? If the latter, I would very strongly recommend you rebook with more margin.