If possible, avoid icy cold water and ice cubes. Such measures could cause further damage to burned skin. Never apply ointment, grease or butter to the burned area. Applying such products, actually confine the heat of the burn to the skin and do not allow the damaged area to cool. After the initial trauma of the burn and after it has had sufficient time to cool, it would then be appropriate to put an ointment on the burn.
Ointments help prevent infection.
In that case, carefully brush the lime off the skin completely and then flush the area with water.