Also, if i supply the lamp with 24VDC but the current the supply can (or will? i think this is where i am cunfused) deliver, will the lamp draw as much current as it needs or will it burn up?
In general, a electrical device does not draw as much current "as it needs". The 'current' that flows through (or into) the device is just determined by the circuitry (aka the electrical components in it), and the components connected to this device..... like external circuitry and components.
It's best to know the electrical specs of the lamp and electrical specs of the source --- such as voltage and current and power ratings --- that would ideally be supplied with an electrical item. Just don't use the device under conditions where the actual values like applied voltage or input current or power are higher than the specified 'rated' value(s). In this way, you can have at least some level of confidence that the item will work properly during its expected operating lifetime.
This also means - in general .... don't use any electrical device where the voltage or current or power exceed rated values.