The Lucky Sandwich is an item in EarthBound. They can be first bought by Ness in a bakery in Onett. They appear consistently throughout the town bakeries, but it also can be bought in the drugstore that appears in the Dusty Dunes Desert. This item is relatively expensive, as it comes to a price of $128. Its primary function is a recover-type item.
Since this is a luck sandwich, it does numerous (and random) things to its user. It can either heal the player from a minimum to a maximum amount of HP, and at times, recovers a party member's PP from a minimum to the maximum. This item is based on the party member's luck, and the higher it is, the successful effect will go to that person.
There are actually 6 different items in the game named "Lucky Sandwich". One is chosen randomly when purchasing this item.
A similar item is the Lotto Meal of Mother 3. This item is purely based on the party member's luck. It can be purchased in a shop in Saturn Valley in Chapter 7 after it is liberated from the Pigmasks for 104 DP or in New Pork City in Chapter 8.