No, the rod with the string dam is pushed up bore with the barrel vertical in a padded vice. The barrel should extend a good 8-10inches above the padded vice jaws so it can be heated in the vice. You can use a propane torch or heat gun for this. A block is put on a stool at the lower end of the lap rod against the handle to keep it in place when the lap is being poured down bore, unto the jag end of the rod. The jag is postitioned about four inches down bore. The lead pot is heated up to about 750-800 degree F. and the barrel is heated while in the vice just before the casting is made. Fill the barrel with a continuous stream of melted lead to just short of the end of the bore so you don't have to trim the lap slug when it cools.
You will also need to make a lap stop to clamp on the far end of the barrel so you don't push the slug out and loose index. If you loose index and can't get the slug back into the barrel precisely in the same position it was cast in then a new slug needs to be made as no two lands and groove are exactly the same around the bore, especially in single point cut rifling but even in the rest of the rifling methods.
I make a lap stop with a piece of angle iron with one end closed off with a flat plate. I leather pad it on the end and in two places on the inside angle then clap it to the barrel with spring clamps allowing about and inch of the lap to extend out before it hits the stop end.
The lap is extended out about an inch into the stop fixture and this is where it is re-charged with fresh lapping compound.