Lime is usually added to acid soils to increase soil pH. The addition of lime not only replaces hydrogen ions and raises soil pH, thereby eliminating most major problems associated with acid soils but it also provides two nutrients, calcium and magnesium to the soil.

Lime also makes phosphorus that is added to the soil more available for plant growth and increases the availability of nitrogen by hastening the decomposition of organic matter.

One common source is wood ashes. The amount of lime to apply to correct a soil acidity problem is affected by a number of factors, including soil pH, texture (amount of sand, silt and clay), structure, and amount of organic matter. In addition to soil variables the crops or plants to be grown influence the amount of lime needed.

Ideally, before you add lime to your lawn you should have a soil test done....but considering that because we put down so much high nitrogen lawn fertilizer that invariably causes the pH to fall into acidic range, liming is generally a good way to increase the pH and derive the benefits of lime.

You should wait about 3 weeks....before....or after...liming a lawn. Lime removes the pH benefit of nitrogen. It would therefore, act against the nitrogen in the make-up of the fertilizer.
This is why bags of fertilizer, bought in the fall for use in the spring, should be placed up off the cement floor of the garage. There is sufficient liming in the floor cement to leach out the nitrogen from the bag. Placed on a wood pallet or a shelf is sufficient to keep the fertilizer safe.

Speaking of wood---cement birdbaths, emptied of their water, can be rested on a piece of wood lumber and left out over winter sitting on the ground. The wood does not draw cold...ergo, the birdbath cement material is not affected by cold.

It take a long time for lime to work its way through the soil structure to be of benefit. Adding the application in the fall then is a good time to do it. Usually, apply it half done in one direction, then the other half in the other direction.
The bag should inform you of how much per thousand square feet.