Pretty sure Reddit can't ban people for promoting/linking to competitors sites as there is EU regulations in place to prevent this.
This issue was raised when Twitter tried to stop people from linking to their Mastodon accounts. Twitter put the policy in place and then quietly removed it soon after.
If you really believe that you were banned for promoting Lemmy then you should mention this in your appeal but as others have mentioned it seems like the issue was spam.
And sure maybe they were waiting for any reason they could get to ban you because you were promoting Lemmy and they got you on spam, always gotta read the contract/TOS to make sure the other party doesn't get you on a technicality