For lentils, there are a few rules of thumb, but not necessarily a hard and fast set of values (like cooking time), because of the natural variability and changes during storage.
But with some minor tweaks, you should be able to significantly improve your results.
First, ratios:
The minimum amount of water you should add is double the amount of lentils. If you plan to drain (and possibly rinse, if the starcy residue puts you off) the lentils, don’t hesitate to go higher, e.g. triple. Especially if you don’t soak the lentils first. If you notice at some point that you underestimated the required amount of water (water level running low but the lentils are clearly not soft enough yet), just top up with more water. You may need a few more minutes in total, but that’s better than burning your food.
Second, stove settings:
Both the starch and the protein can cause the pot to develop foam, spill over and generally make a mess. Therefore choose a pot that’s so large that it’s only half full, perhaps two thirds. Then as soon as the water & lentils have come to a boil, reduce the stove so that the pot just barely simmers. I’m not giving you a number, just observe how the content of the pot behaves. These visual clues will help more than a specific setting, which will get you confused as soon as you use another amount, another pot or another stove.
The foaming is also the reason why I suggest you don’t cover the pot with a closed lid.
Third, cooking time:
This depends on the type of lentils, please check the package, which will often have some sort of information. If not, there are various websites that will provide recommendations. (“Brown” is not precise enough that I would dare to answer here.) a few minutes before the planned cooking time, start tasting a few lentils every minute or so, until they have reached the desired doneness, which is entirely up to your personal preference. Note that value for the next batch, so that you can over time find out which cooking times will give you your preferred results - it’s called “experience” and a good way to learn. You may also find that older lentils (and beans and other legumes) need more time to soften, but that’s perfectly normal.
For the draining in between, I would probably skip that, instead use more water right from the start and strain just at the end, if “sludge” really bothers you, rinse with fresh water (cold to stop cooking e.g. for salads or hot from the kettle to keep them warm). And consider another type of lentil, some will tend to disintegrate! Others hold their shape much better.
If you struggle with maneuvering a hot pot and a sieve, think about either smaller portions (500g lentils it a lot) or a sieve that you don’t have to hold. Sometimes you just need the right tools for the job.
A general bit of advice from someone with four decades of experience: You should monitor your cooking processes carefully while you still develop your cooking skills and instincts. So when you cook your food, stay with it, watch, learn and adjust accordingly.