Lithium lies above sodium in a group and is also smaller in size. According to periodic trend reactivity decreases from left to right in period and down the group.
Reactivity decreases down the group for halogens and increases down the group for alkali metals.
As you have said, Lithium is smaller than Sodium, the valence electron on sodium is further away from the positive nucleus and therefore it has a weaker electrostatic attraction and is more easily lost in a chemical reaction, making it more reactive. This is due to the shielding effect of the second energy level (electron shell) which makes the valence electron on Sodium further away from the nucleus and hence the larger atomic radii.