The lime or other minerals are dissolved in the water, so no amount of filtering will typically help.
Solutions for hard-water involve treating the water in some way. Hard water creates many different problems, and usually toilets are the least-expensive issue. Killing your hot water heater is typically the most immediate side effect, and certainly you'll have scale buildup elsewhere in your plumbing that you don't see. As a result hard-water treatment systems typically treat the whole water supply for the house. There are a few main categories for the most common water-treatment systems:
- Water softening through sodium ion replacement (aka classic water softening systems)
- Reverse Osmosis (typically the most expensive option)
- Water chelation (a more modern method. By way of example this is a chelation system. I've never used it and I'm not advocating for it, it's just less familiar to most so I wanted an example).
In short, hard water sucks. If it is causing problems for your toilet it is causing problems elsewhere, and you might as well treat the whole house (which is pretty much the only option anyway).
Note for apartments: I can't imagine there are any jurisdictions where you would be responsible for fixing this mess. If your toilet is clogging due to build up caused by hard water, that's clearly not your fault or your responsibility if you are only renting. That's not to say that forcing management to fix it is easy, and, not being a lawyer, I'm not sure how this would collide with a lease provision that makes you responsible for clogs (although again, I can't imagine such a provision would apply to clogs like this anymore than it would apply to clogs caused by tree roots). Yell at management until they fix it. If they can't/won't, then it may be time to start apartment hunting the next time your lease is up.