Hi Alan thanks for posting in the community! There currently is not a native way to show the intersection of two lines automatically as you've shown above. If this functionality would be useful to you we'd love to hear more details about your use case in our Product Feedback section Thank you for taking the time to share your feedback!

As a workaround you might find it useful to manually place a dot on your line intersections created by using a standard circle shape and then resizing and styling it accordingly. Please note that in order to do so you'll need to turn off "Snap to Grid" in your settings by choosing View > Grid and unchecking the Snap to Grid option. 

For others with questions about lines please begin by reviewing this Add and style lines in Lucidchart article from the Lucidchart Help Center and post any additional questions below!