You could try using a scatter plot for this. You would need to unpivot your data to match a specific structure. A scatter plot has the option called "Line Connection". Each marker needs to be in a row of its own. You'll need a column to identify the swimlanes. That column can be used in the "Draw a separate line per value in" option in the Line Connection tab.
If you can upload a sample dataset I could help you ot with a sample dxp.