Luck is a stat in the Mother series, appearing only in Earthbound. Akin to IQ, its effects are not completely clear. It most likely affects your accuracy - chance to hit and dodge. Although it may seem that Luck would affect your chance to get a SMAAASH!! attack, it doesn't, as stated by a Friendly Mole in EarthBound.
The HP restored by Lucky Sandwiches is affected by the Luck stat.