The minimum distance you can swim from the outflow depends on so many factors that it's rather hard to offer any sort of helpful advice without studying the specific lake. River volume, outflow size, lake depth near the outflow etc. are all big factors as I'm sure you know.
If the lake is fairly deep you can often get pretty close, but the lack of certainty + lack of room for error necessitates an ample safety margin. One concern I'd have is that the safe distance might not be constant across the lake. With varying water depths and water body shapes, some areas may have more pull than others.
I'd try to keep your options open. If you arrive at the lake and examine the situation, you may very well find there is a water crossing route that is safe enough and keeps your swim to an acceptable length. Your experience and risk tolerance come into play in evaluating. You might not like the look of the crossing though, so it's prudent to be as prepared as possible for other options like going around the lake and even turning back. If you haven't done your research on routes around the lake and you don't have enough food to turn back, then you may be tempted to attempt a swim that you're not comfortable with.
I would prepare for this by seeing how long (time and distance) you can effectively swim in various water temperatures. If you measure the temp at the lake, you can get a good idea of how your body will hold up if you've already experimented at that temp.
In terms of gear, there's a lot of options ranging from nothing to a full on packraft. In between, you've got aids like inflatable PFDs, sleeping pads, neoprene clothing, wetsuits, pool toys etc. I'd probably take a FlytePacker raft + trekking pole paddle blades.
Swims are usually longer than they look.