Yes, you can connect your LMN with Quickbooks remotely but you must make sure that the LMN QB Sync application is downloaded onto your server or it will not work.
The critical thing here is that LMN's QB Sync tool needs to get installed somewhere where it has LOCAL access to the server. So, when a user has a server on their own network, you can install LMN Desktop sync on the desktop because it can connect to the server locally (e.g. L:\ or \AccountingServer)
When its on a cloud server, you connect via remote desktop, not through a local network. SO - the user has to be absolutely sure that the hosting company will let them install the LMN QB Sync tool on their web server. Some will, some won't (for security reasons).
Please check out this host if Intuit won't offer the service: http://www.cloud9realtime.com/quickbooks-hosting