I do not believe there is a way to do this in the swimlane itself. However this is a field that you can add to the Card Layout: Board -> Configure -> Card Layout. From there you can choose to add the "Fix Versions" field to either the backlog/active sprint or both. This is one way to be able to see that field on the cards that appear on that board.
However it does not appear possible to display this in the exact section you specified in your screenshot. But I hope that adding this information to the card itself might still provide some helpful information for you here.
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