Abaixo está um script que eu encontrei e usei com sucesso no passado, para roubar espaço de uma partição / tmp e adicionar a outras partições. Use o Guia de Administração do LVM mencionado nos comentários anteriores e adapte o seguinte para atender às suas necessidades:
#!/bin/sh
#
# Script to re-allocate space from tmpVol to auditVol and varVol
#
################################################################
ROOTVG=VolGroup00
TMPVOL=${ROOTVG}/tmpVol
VARVOL=${ROOTVG}/varVol
AUDVOL=${ROOTVG}/auditVol
# Verify that /tmp is now of type "tmpfs"
df -Pt tmpfs /tmp > /dev/null 2>&1
if [ $? -ne 0 ]
then
echo "/tmp is not of type 'tmpfs'. Exiting..."
exit
fi
# Compute blocks for re-allocation
FREEVOL='lvdisplay ${TMPVOL} | awk '/Current LE/{print $3}''
HALFREE='expr ${FREEVOL} / 2'
# Nuke the old /tmp volume
lvremove -f ${TMPVOL}
# Resize the remaining logical volumes
lvresize -l +${HALFREE} ${VARVOL}
lvresize -l +${HALFREE} ${AUDVOL}
# Resize the filesystems
resize2fs /dev/${VARVOL}
resize2fs /dev/${AUDVOL}