from official docs as in https://docs.lizmap.com/current/en/install/py-qgis-server.html#adapt-the-lizmap-web-client-configuration
for py-qgis-server:

First of all, we create an environment file /srv/qgis/config/qgis-service.env with

LC_ALL=en_US.UTF-8
LANG=en_US.UTF-8
DISPLAY=:99
QGIS_OPTIONS_PATH=/srv/qgis/
QGIS_AUTH_DB_DIR_PATH=/srv/qgis/
GDAL_CACHEMAX=2048
QGIS_SERVER_CACHE_SIZE=2048
QGIS_SERVER_LIZMAP_REVEAL_SETTINGS=TRUE
QGIS_SERVER_FORCE_READONLY_LAYERS=TRUE
QGIS_SERVER_TRUST_LAYER_METADATA=TRUE
QGIS_SERVER_APPLICATION_NAME=qgis-server

lacking of setting of

QGIS_SERVER_PLUGINPATH=/srv/qgis/plugins (or whatever your Lizmap server plugin resides in your sys)

that seems to be a mandatory setting in order to make py-qgis-server to works!