David - Squeaky sound

What you are hearing is new metal on wood and it just needs some non oily lubricant - best to use dry Teflon spray (PTFE spray).

The source of the squeaking can be at the cams at the top right of the castle below the shelf. Carefully apply some lubricant on the axle between the each of the cams . You can use a cotton swab . 

Another source of the squeaking can be the connection between the lamm and the loom. Pull the axle of the lamm out of the hole, add a little lubricant on the end of the lamm or rub a bar of soap over the end of the lamm (as a lubricant) and put it back in.