The alternator on your tractor is not like a conventional alternator like the one that is in a car. The alternator is located underneath the flywheel. There should be wires coming off of that location. Those should be the alternator wires. If you have a multimeter, check the current of the wires when the tractor is running. If it has power, it may just be your battery. If it doesn't have power, the alternator is worn out and should be replaced.
No reason to check current when checking voltage is much quicker and easier. I'm not trying to "shame" you by any means, but the words current and voltage tend to get used interchangeably when they aren't the same thing.
Current refers to the amperage of an electrical circuit whereas voltage is... well, the volts. Coincidentally, even though water and electricity are typically not a good combination, water flowing through a pipe is a great analogy for how electricity (in particular with DC applications) works. You can think of the water itself as current (amps). You can put water in a pipe, but unless it has pressure, it's not going to flow, right? In an electrical circuit, voltage is the pressure that causes the amps to flow. Likewise, the more pressure you apply to the water, the more water will flow through the pipe in a given amount of time, correct? Amperage is the rate at which voltage is flowing.
Voltage and current are directly proportional, meaning a drop in one will result in an equivalent drop in the other. This means that, in most cases, you can measure voltage and determine how much current is flowing. If, for example, you're supposed to have 16 volts coming out of an alternator and you only read 10 volts, the alternator is only producing enough current to generate 10 volts of output.
Make sense?
On to the original post: it's possible the work lights you added are drawing too much current for the stator (alternator) to keep up. A quick, simple test would be to disconnect 1 of the work lights and see if it runs longer. If it does run longer (even by a few minutes), disconnect a 2nd light (removing the bulbs will be the easiest way to do this) and see if it runs longer than with 2 lights connected.
If you find this to be the case, buy some lower wattage bulbs. They may not be as bright as you'd like, but they won't kill your engine either.