The first place to troubleshoot is the doneness of the custard.
"Time in the oven" is a very bad way to judge when to stop baking. It can be wildly off. The only certain way is to measure the internal temperature.
Make it again, using a digital oven thermometer, and take it out at maybe 85 Celsius. The optimal range for custards is 83-87, but you want to avoid overheating it, and there can be a bit of carryover, so it's best to stay in the middle of the range. Also, make sure it's fully set before cutting, so leave it overnight in the fridge.
Only if the above doesn't work, should you try finding a better-working recipe. You can also tweak on your own, but that's usually more work than trying out a few existing recipes until you find a good one. If you do tweak, the most promising direction is to increase the ratio of egg whites to egg yolks. This will change your taste away from typical lemon curd, but will also give you a firmer custard, yolky custards tend to be smeary. So maybe 5 whole eggs and 6 yolks would be a good place to start. If the egg whites aren't enough for a good tweak, I'd start reducing the sugar.
Can I simply add more eggs/egg yolks
At that high amount of eggs, I wouldn't try adding even more. The ratio of yolks to whites can be a good thing to change though, see above.
Will more butter create a stiffer custard when cooled?
No, it will create a softer custard.
Does the acidity of the lemon juice influence the stiffness?
Potentially yes, but it's complicated. You don't need any acidity to get a firm custard with eggs, they work all on their own. In a lemon curd, the acidity does change the texture, but the larger problem is in reducing its curdling properties, else you'll end up with a grainy mess. So you don't want to go that route, it will be very complicated if it works at all.
