I was wondering if a player who plays first strike may choose to evade the initiator's battle back.

For example, suppose a pack of medium cavalry declare close combat on a group of light cavalry. The defending player now plays the "first strike" card and no flags are rolled against the medium cavalry.

May the light cavalry now declare an evasion on the medium cavalry's roll?

While playing the game, I felt that the light cavalry may not evade.

Your feeling is correct.

If your unit is using First Strike then it is having it's Battle Back before the initial attack
and the Special Actions rules state: An evading unit may not Battle Back.

Phill