My Leopard Gecko barely survived 2 days with no heat source can it live without heat or no?

No, they NEED heat as a bare necessity to live

It needs heat only if it has eaten recently. If it cannot warm up then the food will rot in its stomach and it will be killed as a result. If it has not eaten for a while, then there is nothing to worry about, unless the temperature drops below freezing. Of course, if it is exposed to cold temperature for months, it will have no appetite and may starve to death.

Well, it depends on what your climate is like, but they're desert dwellers, so they're used to warm conditions, and their metabolism and ability to function requires them to be at a certain temperature. If they fall below their optimum temperature, they'll be sluggish and have issues functioning normally, and if they fall too much below that temperature, their vital systems will start to shut down. So unless its reasonably warm where you are year round, you'll need to provide some sort of a heat source.