Can Relentless Gaze of the Sun usefully Repeat a Power Card with Relentless Punishment if the first use makes the land untargetable for the second use? (e.g., if Lure of the Unknown Gathers a Town into a land, preventing that land from being a land without Invaders.)

Can Relentless Gaze of the Sun usefully Repeat a Power Card with Relentless Punishment if the first use makes the land untargetable for the second use? (e.g., if Lure of the Unknown Gathers a Town into a land, preventing that land from being a land without Invaders.)

Yes. When the source of a Repeat specifies which land it affects, ignore the normal Range and Target requirements. In this case, the second use of Lure of the Unknown can Gather an additional Explorer/Town, since the "no Invaders" targeting condition is ignored.
This won't let you get around any conditional requirements in the Power's effects though. For example, if Sear Anger Into the Wild Lands destroys the last Invader in a land, a Relentless Punishment Repeat of the Power can no longer meet the "if Wilds and Invaders are present" condition in the Power's effect to add more Fear.