No. The Nintendo DS/DS Lite only runs games from official Game Card cartridges (Slot-1). Memory sticks (SD, Memory Stick Duo, USB drives) cannot be used to boot games on stock hardware.
Devices like R4, Acekard, DSTT, SuperCard DSTWO fit in Slot-1 and read microSD cards with ROMs. These are unauthorized and primarily used for piracy; they also violate Nintendo's Terms of Service and can brick your system if firmware updates conflict.
Stick to legitimate cartridges or the 3DS eShop for a safe experience.