If Lobot is in an engagement with an undamaged Executor , does Executor 's power "cannot be targeted by enemy card effects" also protect against Lobot 's power to treat all combat icons as edge-enabled?

In other words, does Executor keep its 3 edge-independent unit-damage even if DS loses the Edge battle?

In other words, does Executor keep its 3 edge-independent unit-damage even if DS loses the Edge battle?

No, it doesn't. The Executor can't be targeted by enemy card effects (Rebel Assault), cards that don't make you specify a target can still affect the Executor (Lobot, X-Wing Escort).

Lobot doesn't Target. So yes it works fine.

Thanks for the clarification.

That "target" specifier is an interesting detail. And it makes Lobot even more interesting to play.