The command I tried is:
lighthouse <URL> --perf --output json --output-path=./report.json --save-assets --disable-cpu-throttling --disable-network-throttling --disable-device-emulation --verbose --chrome-flags="--load-extension=<PATH_TO_EXTENSION>"

This does not enable the extension as I can see in the logs that extensions are disabled by default:
ChromeLauncher:verbose "/usr/bin/google-chrome-stable" --disable-translate --disable-extensions ...