In لَمْ يُسْرِعْ بِهِ نَسَبُهُ, لَمْ precedes an imperfect verb and makes its meaning negative: lineage did not carry the person forward. The final sukūn in يُسْرِعْ reflects the jussive construction.
The teaching strikes a balance: benefiting from virtuous ancestors is good, but their names cannot substitute for honesty and effort.
A person’s value should not be reduced to social prestige while their actual conduct is ignored.