Is what I vowed, to provide a dinner meal for seven of my friends if my mother recovers, considered a vow, and is it permissible to substitute it with a lunch meal?

If you intended to offer dinner only to your friends, this falls under a vow concerning permissible acts (نذر المباح), regarding which there is disagreement among scholars concerning its validity and binding nature. The preponderant opinion is that it is not binding; therefore, nothing is obligatory upon you, whether you fulfill your vow or not. However, according to the other opinion, you have the choice between fulfilling the vow or offering expiation for an oath (كفارة يمين). The fulfillment would be by offering dinner, not lunch, unless your intention was merely to provide food.