Testing for low voltage,, Start with the main panel in the barn,, Take the cover off put your meter on 600v ac check between each hot wire going into your main breaker to the neutral wire you should have around 120v on each,, Then plug in your 2- 250 watt lamps and test again,, If the voltage stays the same then the problem is not outside the panel.. Lets assume all is OK there,, Unplug the 2 lights and check the voltage coming out of your 120 breakers,, " I assume you have more than one? " See if the voltage is still 120v between the breakers and your neutral .. then plug in your 2 lights and check the breakers again...
Start with that and let us know what you find,,