In this case, it may be impossible to determine. Unfortunately, we simply do not know the nationality of the colt's owners. Were the owners Greek, we would assume the conversation was in greek and simply consult the text which uses the word Κύριος which means "master" or "he to whom a person or thing belongs." Therefore in Greek, it does not read that God has need of the colt. Despite this, When the Tetragrammaton is translated into Greek, Κύριος is the word used, but if translating from Greek back to Hebrew, this is not necessarily the case.
Therefore, were this conversation to have been in Hebrew and were we party to it or were the text in Hebrew, the answer could be very simple because it could read Yahweh. On the other hand, it might not be very simple as the word Elohim was often used which could indicate either the divine or an earthly lord. Were this the case, then we would have no clearer answer in the Hebrew. Simply put, if we presume the conversation was in Hebrew, but translated to and recorded in Greek, Since we are dealing with the ownership of the Colt, it is just as reasonable to conclude that the owner of the donkey has a need for it as it would be that Yahweh needs it and there is no way to know which interpretation is correct (or if both are correct.)
Finally, Jesus would have spoken Aramaic and so did his disciples, but again, we have the same problem with Aramaic as we do with the Hebrew tounge.