Thaw lumpia wrappers if frozen. Lay several wrappers on a clean, dry surface and cover with a damp towel to prevent wrappers from drying out.

Mix beef, pork, onion, green pepper, and carrot together in a medium bowl. Place about 2 tablespoons of meat mixture along the center of a wrapper. Do not overstuff wrappers or they will burn before the meat is cooked. Fold one edge of the wrapper over filling. Fold outer edges in slightly, then roll into a closed cylinder. Wet a finger with water and moisten the outer edge to seal. Repeat with remaining wrappers and filling, keeping finished lumpia covered to prevent drying.

Heat oil in a 9-inch skillet on medium to medium-high heat until oil reaches 365 to 375°F (170 to 175°C). Fry 3 to 4 lumpia at a time, turning in oil until nicely browned, about 2 to 3 minutes per side. Drain on paper towels.