What home treatment can be done for a mild degree of frostbite? Lukewarm bath?

Yes. Gradual warming with water 104 to 107 degrees farenheit with no direct heat source exposure as part can be numb and get burned. Also recommend Motrin or NSAID to control inflammatory intermediates that can produce more damage.
Yes if mild. Minimal frostbite can be helped with warming the areas and gentle massage. Should seek medical guidance if you are not certain about the extent of the injury. Can be difficult to judge in some cases.