O crescimento de um volume quase nunca resultaria em perda de dados. É extremamente confiável. (Mas você recentemente verificou backups, não é? Nunca há garantia.)
Para aumentar para todo o seu espaço disponível:
lvresize -rl +100%FREE /dev/vg_proxy/lv_root
Ou para crescer para um valor absoluto / relativo:
lvresize -rL 30G /dev/vg_proxy/lv_root
lvresize -rL +5G /dev/vg_proxy/lv_root
O significado é um pouco diferente. Mas é assim que costumo usar as duas opções. Você pode ler mais na página man.
-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] Change or set the logical volume size in units of megabytes. A size suffix of M for megabytes, G for gigabytes, T for terabytes, P for petabytes or E for exabytes is optional. With the + or - sign the value is added or subtracted from the actual size of the logical volume and rounded to the full extent size and without it, the value is taken as an absolute one.