Swap inside VMs is completely independent of swap on the host. If the OS inside the VM was configured to use swapping (as many installers do automatically), it will continue to swap as before. If you want to disable it there as well, you generally can use the same approach as for your host.
When using LVM there is a "swap" LV used. So your VG would need some unallocated space and then you could use lvresize to resize that "swap" LV and later format the LV with mkswap.
Another option would be to add an additional swap file.