You can try using a different account. This wouldn't work if they banned you based on your IP or Unique User ID (it's a randomly-generated string associated with the account you paid for, which means it doesn't matter what IGN you set yourself as), though.
If you've been banned it's likely against the server rules to log in on a different account, known as ban evasion, and doing so will get your other account banned as well. Also, if you disagree with the staff and owner in such a way I recommend you seek out another server.
"Kicked whilst connecting to lobby" doesnt automatically mean ban, is is just problem with connecting, but if it says you havre been banned or something like that after that, they just dont want you there and you should not try to even bypass this. Just find different server.