Как я могу изменить размер своего логического тома в CentOS6?

Growing a volume would almost never result in data loss. It is extremely reliable. (But, you do have recently verified backups, don't you? There is never a guarantee.)

To grow to all of your available space:

lvresize -rl +100%FREE /dev/vg_proxy/lv_root

Or, to grow to an absolute/relative value:

lvresize -rL 30G /dev/vg_proxy/lv_root
lvresize -rL +5G /dev/vg_proxy/lv_root

The meaning is somewhat different. But, this is how I usually use the two options. You can read more in the man page.

-l, --extents [+|-]LogicalExtentsNumber[%{VG|LV|PVS|FREE|ORIGIN}] Change or set the logical volume size in units of logical extents. With the + or - sign the value is added to or subtracted from the actual size of the logical volume and without it, the value is taken as an absolute one. The number can also be expressed as a percentage of the total space in the Volume Group with the suffix %VG, relative to the existing size of the Logical Volume with the suffix %LV, as a percentage of the remaining free space of the PhysicalVolumes on the command line with the suffix %PVS, as a percentage of the remaining free space in the Volume Group with the suffix %FREE, or (for a snapshot) as a percentage of the total space in the Origin Logical Volume with the suffix %ORIGIN. The resulting value is rounded downward for the substraction otherwise it is rounded upward.

-L, --size [+|-]LogicalVolumeSize[bBsSkKmMgGtTpPeE] Измените или установите размер логического тома в мегабайтах. Суффикс размера M для мегабайт, G для гигабайт, T для терабайт, P для петабайт или E для эксабайт не является обязательным. Со знаком + или - значение добавляется или вычитается из фактического размера логического тома и округляется до полного размера экстента, а без него значение принимается как абсолютное.

man lvresize