I own two lemons cars and provide arrive and drive services for races more or less Nationwide. If you are serious about trying it, I have a car that is specifically built for new racers experimenting with the series
There are a group of people who tend to do well in the local races. They are proficient because of their organization and understanding of what it takes to win an endurance race. If you're trying to win right off the bat, this isn't the series for you. Lemons is one of the most difficult series to score an overall victory in (I have done so ten times in approximately ten years of managing teams).
Luckily, there are classes and other awards to win, which recognize the effort people put in to these cars.
A few bits of advice:
Unless you're a professional cage builder, don't build your own cage. I don't care how good of a welder you are. Cage design has many facets, and the rules governing a Lemons cage are different than other sanctioning bodies. If you're familiar with an SCCA or NASA cage, then go ahead. Otherwise, think twice.
It will cost $4000-$6000 to build a car. There are expenses beyond the car and cage. You need a proper seat. You need proper belts. You need to do proper prep on your car. Read the rule book carefully. Wheel bearings, brakes, tie rod ends, ball joints and similar parts are exempt from the $500 purchase price. This is because you need to make sure you don't lose a wheel and kill someone as it crashes through their windshield. Your seat can save your life, or kill you depending on installation. Your seat belts need to be high quality and easy to adjust and fasten. You need new, well installed fuel lines.
There are other expenses that come with the race. You need a HANS type device to share between your team. This is a little tricky because they are sized. If you have drastic differential in body type, you need more than one. You need a race suit for each driver. This is your last line of defense between you and a car fire. Don't cheap out. You need a helmet, which is a different type than a MC helmet. Just like bike helmets, there are basic standards, and then there are things like comfort that will factor in to your overall experience.
When you race you need a trailer, either rental or own. You should not plan to drive to car to and from the track. You need fuel cans. You need a way to buy fuel and bring it to the track. Likely in the neighborhood of 50 to 100 gallons. You need cans to fuel the car quickly and safely, without spilling everywhere. You need spare parts, because things will break.
You need tires. Tires are budget exempt. You can buy cheap tires, but they will chunk and fail when you push them on track. You need two sets of wheels minimum. Three sets if you want plan to caro rain tires.
There are many many many other needs, but these are basics.
With all that said, go for it. Read the rules, do real research, and spend all the money you can afford on safety equipment and brakes.