Hi @robinmartin ,
Try inserting the headphones into the laptop and then gently, stress very gently, wriggle the plug up and down and side to side whilst removing and inserting the plug a few times. and check if this resolves the problem.
There is an internal contact in the headphone socket which is operated by the insertion of the headphone cable plug. When operated it signals the BIOS to disconnect the audio from the laptop speakers and direct it to the headphones. Sometimes this contact can get temporarily stuck in the operated position or worst case it gets bent out of shape and stays operated.
If doing the above doesn’t work you may have to replace the audio port board.
Here’s the hardware maintenance manual for the laptop.
Go to p.53 to view the necessary pre-requisite steps and then the procedure to remove the systemboard. This will give you access to the audio ports board
The supplier linked was only to show you what it looked like and the approximate cost. There are other suppliers online that may suit you better. Just search for Lenovo G570 audio ports board to get results.
Note: When searching for the board I noticed that there seems to be 2 board options. One has a part number of LS-6756P and the other is LS-6751P. If you need to replace the board then you may want to verify which one is in your laptop before ordering. The part number is printed on the board itself. If you zoom in on the part that I linked you can see the part number.