LVM does not use partitions.
The logical and physical layers must be delt with from the top down.
LV's may need to be removed or moved, swap f/s on LV may need to be deleted and recreated.
As you can see, diskspace and dual booting is planed before the fact.
The mounted f/s can not be reduced so a Live CD system is needed.
# boot systemrescue dolvm
size must be consistent.
On the unmounted f/s using the space wanted.
resize2fs /dev/VG-LV fssize
On the LV using the space wanted
# lvm lvresize --size lvsize /VG/LV /dev/sdxn
on the PV using the space wanted
pvresize --setphysicalvolumesize pvsize /dev/sdxn
on the Linux partition type 83
change partition to new size, save, quit
Do the Math