Assuming that the 4,000 lbs weight is dry, once you add water in the tanks, food, equipment and supplies the loaded weight of the trailer is going to hit the 5,500 lbs or more. Just because the hitch is rated for 6,000 doesn't mean that increases the towing limit of 5,000 of the vehicle. The ratings are determined on many factors, weight, tires, brakes, engine etc. It isn't what you can pull it also is what you can stop. Add weight for additional persons, gear, accessories, bumpers, winches, sliders and tongue weight you are going to exceed the 6,525 lbs GVWR or the GAVR of 3,970 of the rear axle of the LC. A stock 80 starts out at ~4,800 lbs.
Towing 4,000+ lbs through anything other than flat ground is going to be ugly. If you do get up to speed before a long grade like you would find on I40, if you get slowed by another vehicle or traffic you will never be able to get back up to speed. Then with a travel trailer you got take into account additional losses from the high profile of a travel trailer, windy conditions etc. Lastly you would be lucky to get 9 MPG or less on average.