It should not matter how the agent script is executed - be it xinetd, systemd socket, or ssh. But you probably have to run it as root (directly or using sudo) to be able to gather all the information.
You can try sudo /usr/lib/check_mk_agent/plugins/lvm to see the information returned by the lvm plugin.
Here’s a sample output from a VM with 2 volume groups and 6 logical volumes:
<<<lvm_vgs>>>
vg0 1 5 0 wz--n- 17175674880 2143289344
vg1 1 1 0 wz--n- 26839351296 0
<<<lvm_lvs:sep(124)>>>
lv_home|vg0|-wi-ao----|2147483648||||||||
lv_root|vg0|-wi-ao----|4294967296||||||||
lv_swap|vg0|-wi-ao----|2147483648||||||||
lv_tmp|vg0|-wi-ao----|2147483648||||||||
lv_var|vg0|-wi-ao----|4294967296||||||||
lv_data|vg1|-wi-ao----|26839351296||||||||