I've been pondering. If you want to go from this:
the only option is basically to over-lengthen, then break out (trim, whatever).
How about an option to Lengthen that, instead of specifying an exact amount to lengthen by, would interactively follow the path of the lengthened entity, and, along the way, use usual snap rules, thereby achieving the example above precisely yet in one step?
As Lengthen works with arcs too, it would by nature work with arcs as well.
(BTW, why does Lengthen not work with ellipse segments? Just curious.)