I dont know if it will help but
There is a section on LVM. It doesn't seem to work all the time and haven't figured this out yet.
I cant be responsible if you mess up your system. At least the commands are there for your reference.
I think you need to :
create a physical volume on that free partition with pvcreate
extend your lvm group with vgextend
extend your logical volume with lvextend
resize your fs