Does a spell that says 'counter target spell' work on a spell that is already resolving?

A counterspell targets a spell that is on the stack. Once a spell begins resolving, it leaves the 'on the stack' zone and its resolution is carried out — it is no longer a legal target for any spell or ability that says 'counter target spell.' (CR 608.2)

The window to counter a spell is before it resolves. After all players pass priority in succession without taking any action, the topmost object on the stack begins resolving. At that moment, players can no longer respond to it with a counterspell. (CR 116.3, 509.1)

Additionally, CR 608.2b specifies that if a spell's targets become illegal before it resolves, the spell is countered — but a resolving spell itself is no longer a valid target to begin with, so this rule never even comes into play for the resolving spell.

Concrete example: Your opponent casts Lightning Bolt. You let it resolve without responding. The moment it starts resolving (dealing 3 damage), you cannot cast Counterspell to stop it — the opportunity to counter it has passed. You needed to cast Counterspell while Lightning Bolt was still on the stack and before both players passed priority.

In short: counterspells must be used during the response window, while the spell sits on the stack awaiting resolution. Once resolution begins, that window is closed.