how to synchronize bungeecord permissions on luckperms?

Read
https://github.com/lucko/LuckPerms/wiki/FAQ#where-do-i-install-luckperms
https://github.com/lucko/LuckPerms/wiki/FAQ#can-i-just-install-luckperms-on-bungeecord
and maybe
https://github.com/lucko/LuckPerms/wiki/FAQ#how-do-i-get-permissions-to-sync-across-multiple-servers
and https://github.com/lucko/LuckPerms/wiki/Network-Installation

Just connect to the same database and use /lpb sync and /lp sync

/lp networksync to synchronize the whole network, but with bungee messages configured you don't even have to, as it will be synchronized automagically ;)

Will this work between the permissions within the bungeecord config.yml and luckperms?

You can enable the following option in the config.yml of LuckPerms-Bungee, to apply permissions and groups from the BungeeCord-config:
https://github.com/lucko/LuckPerms/blob/master/bungee/src/main/resources/config.yml#L160