I had not heard of chalazions before. It got me thinking that what you have sounds a lot like what I have - blepharitis. The lumps on the lids, the itchiness, etc.
What blepharitis is is inflammation of the eyelids. It usually affects the edges of the lids. It's not thought to be serious, but for those of us with it, it can and does become uncomfortable. I have it on both eyes. I also have styes on occasions which present in a different way.
The way blepharitis affects me is my eyelids get a little sore to start with and itchy. Then tiny lumps appear, normally yellowy looking and quite hard. I have learned these are caused by the sebaceous glands filling with an oily fluid. If they get infected then this can cause a stye. Tiny skin flakes sometimes appear on my eyelids too. Of course, I scratch my eyes, totally wrong thing to do. Sometimes my eyelids stick together, particularly on waking in the morning.
It is thought that patients with blepharitis make less tears than normal - I have Sjogrens so this sounds right to me. The exact cause is not known. It tends to 'flare-up' and then ease off in severity. If you have blepharitis, you are likely to always have a tendency to have it. Sometimes a 'vicious cycle' may play a part. For example, your eyelids may become slightly inflamed and itchy. You may then rub them - which makes the inflammation worse. This in turn can lead to your eyelids becoming sore. You may then keep rubbing them further, which leads to more inflammation, and so on.
What I use and find the best thing is witch hazel. I use cotton buds, (not sure what they are called in the US) - dip one end into the witch hazel and wipe along the very edge of the top lid. I then use another to do the bottom lid. I repeat this with the other eye. Never use the same cotton bud on top and bottom lids, nor on ech eye. Always change for each lid - 4 in total. It really eases the itching and helps to release the debris that is inside the little glands. Only my own way of dealing with this, but it does work for me.
Baby shampoo was suggested, but I personally can't see how putting shampoo near your eyes would stop inflammation and itching, and surely it would irritate your eyeball, so I have never tried it.
If the treatment is used as soon as the problem starts, then none of the nastiness usually occurs for me. Sometimes though I admit I get a little "oh, I'll do it later" then this makes thing worse of course.
Hope this helps. Take care.