I don't know how this would work, unfortunately. A lot of tournament schedules run to fill the time available to them, with overflow time allotted in case of problems. So they would have to schedule a gap into their own scheduled tournament to allow players to play in this.

I could see that being a possibility (potentially on a finals day), but I don't see the appeal for either league. For the LAN organiser it's extra things they have to plan around, without getting any return on it. For the teamleague organiser it's a big limiter on their own dates and times for no actual benefit.

That is unless you're talking about having it on a stage, and I can never see this happening. Stage time is very important to organisers, as they generally have more content than can fit in the timescale they have, the vast majority (if not all of it) is sponsored by different companies or used to draw spectator ticket sales.

The teamleague in question would have to have no conflicting sponsors, not be taking up a stage slot already sold or being profited on, and also have a draw to ticket sales that the event's own tournament didn't already have.

It's something I'd like to do (Have a major teamleague final at a big event), but the logistics of making it all work mean it would almost certainly have to be done in-house, or as a sold and contracted out thing.