Get help diagnosing and treating a sick plant. Include pictures, watering schedule, light levels and temperature/location so that we can help figure out what's wrong.
They shouldn't hurt it.Mushrooms are growing because spores made it into your potting mix and the conditions are right. It has more to do with the soil vs the plant, but some say it can be beneficial to the plant. At the very least it shouldn't cause harm and you can remove the mushrooms if you don't like them. If you want any to get rid of them, repot into a new medium.
The mushrooms themselves are probably harmless, however they might be a sign that the soils too damp. Citrus like loose airy soil, if the soil is too dense or soggy their roots can suffocate.
I usually use a "near hydroponic" potting medium made of three parts perlite, two parts fine pine bark, one part peat moss for my citrus. The advantage is that it's nearly impossible to over water, it does have a downside of being nutritionally barren, so most nutrients have to come from fertilizer.
All that being said, that lime looks pretty happy. So I wouldn't worry unless it starts dropping leaves and having the branches die back.