That doesn’t really look like a swim lane diagram. In a swimming pool, swimmers are generally supposed to go along the lanes, not across them.
What you show looks more like what we call layer bands. See for example Layer Bands using a Background Part, although there the direction of growth is towards the right so the bands are vertical. In your case it appears that the direction of links generally goes downwards so the bands are horizontal.
I don’t know if TreeLayout is appropriate for your app – it depends on what the link relationships are. You can implement layer bands in other layered layouts, including LayeredDigraphLayout.
Might there be some nodes in each layer that do not have any connected links at all? If so, will you be providing that information in the model?