What I have used:

LuckPerms v4.3.7 on a Spigot-Server 1.8.8
Luckperms is connected to a MongoDB

/lp info
[LP] Running LuckPerms v4.3.7 by Luck.
[LP] -  Platform: Bukkit
[LP] -  Server Brand: CraftBukkit
[LP] -  Server Version:
[LP] -  git-PaperSpigot-"4c7641d" (MC: 1.8.8) - 1.8.8-R0.1-SNAPSHOT
[LP] -  Storage:
[LP] -     Type: MongoDB
[LP] -     Ping: 1ms
[LP] -     Connected: true
[LP] -  Messaging: None
[LP] -  Instance:
[LP] -     Static contexts: None
[LP] -     Online Players: 1 (0 unique)
[LP] -     Uptime: 10m 16s
[LP] -     Local Data: 1 users, 1 groups, 0 tracks

Plugins:

/pl
[15:03:22 INFO]: Plugins (1): LuckPerms

Config:

# Defines if "opped" players should be able to use all LuckPerms commands by default.
#
# - Set to false to only allow users who have the permissions access to the commands
commands-allow-op: false

What I did:

I set up a new server and connected LuckPerms to an empty Mongo database. Then I set the setting "commands-allow-op" in the config to false.

Then I tried to access the LuckPerms Commands without Op. Which of course didn't work.

/lp creategroup test
[LP] Running LuckPerms v4.3.7.

Then I tried to access the LuckPerms Commands with Op. What shouldn't actually work.

/lp creategroup test
[LP] test was successfully created.

The problem:

I may misunderstand your function in the config. But if I understand it right it shouldn't work with Op.

Did you actually restart the server, after you changed the settings?

Did you actually restart the server, after you changed the settings?

Yes of course.

I can't reproduce using a totally new server.

Perhaps you assigned some permissions to yourself by mistake?

@lucko

I tried again. Please change the following and try again.

# If the plugin should apply Bukkit default permissions.
#
# - Plugin authors can define permissions which should be given to all users by default, or setup
#   permissions which should/shouldn't be given to opped players.
# - If this option is set to false, LuckPerms will ignore these defaults.
apply-bukkit-default-permissions: false

Well yeah, it's obviously not going to work if you disable that option too - the comment makes that very clear. :)

@lucko
It is not possible to leave LuckPerms out of this setting, because I want to use this setting.

No, LP uses the "bukkit default permissions" system to implement the commands-allow-op setting.