The primitive that locks some resource for limited amount of clients is called a semaphore.
It's easily implemented with a buffered channel:
var semaphore = make(chan struct{}, 4) // allow four concurrent users
func f() {
// Grab the lock. Blocks as long as 4 other invocations of f are still running.
semaphore <- struct{}{}
// Release the lock once we're done.
defer func() { <-semaphore }()
// Do work...
}