Read and write to a file while keeping lock

I am making a simple page load counter by storing the current count in a file. This is how I want to do this:

1. Lock the file (flock)
2. Read the current count (fread)
3. Increment it (++)
4. Write new count (fwrite)
5. Unlock file/close it (flock/fclose)

Can this be done without losing the lock?

As I understand it, the file can't be written to without losing the lock. The only way I have come up with to tackle this, is to write a character using "r+" mode, and then counting characters.