what are benefits of lime in compost

Lime was traditionally used on land that had been composted previously as it helps release nitrogen into the soil. I'm not sure of the chemistry of the reaction, but you have to be careful not to over-lime as this can lead to impoverished soils. In compost (I assume you mean the compost heap or manure?) it is used as a 'sweetener' as it prevents the compost from being too acidic. Compost is best broken down by aerobic organisms and worms, and these don't like conditions which are too acid. If you don't lime your compost heap it can become quite smelly and anaerobic and produces a slimey mass rather than something crumbly and friable.