Flexor digitorum profundus is responsible for flexion of DIP. Medial aspect of the muscle (which flexes the 4th and 5th digit) is supplied by the ulnar nerve (C8, T1). The lateral aspect (which flexes the 2nd and 3rd digit) is innervated by the median nerve specifically the anterior interosseous branch (C8, T1). So the question is describing a laceration damaging the nerve supply to the DIP flexor of the 2nd digit (index finger). This is saying the medial nerve is being damaged (C8 and T1; lower trunk roots).
Lumbricals (1st/2nd, median; 3rd/4th, ulnar) are a group of muscles that flex at the MCP joint, and extend PIP and DIP joints.
Could remember as 'flexor digitorum profundus is profoundly long' since tendons insert on DIPs. Compared to flexor digitorum superficialis whose tendon wraps around profundus' superficially but inserts on PIPs.