I think I found a useful workaround to the lack of a feature to add red connection points to a shape: Create a tiny shape like a tiny rectangle place it where you want the connection to be and arrange it with Send to Back so it isn't visible. Then Group it with your custom shape and save the group. If you drag a line near the little invisible rectangle the connection point on it will appear. You can attach your line and the line will move if the shape moves. There may be some gotchas to this approach but it's working for me. Maybe someone who knows Lucidchart better than I can comment on whether this is a good approach or not.
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