Baelish has the title of Lord because he inherited it: “Lord Petyr’s father had been the smallest of small lords, his grandfather a landless hedge knight; by birth, he held no more than a few stony acres on the windswept shore of the Fingers.” Here’s the thing about lordship – lordship is a social and legal status that affords you certain privileges, like the right of pit and gallows. It is not dependent on wealth, beyond an absolute minimum of land.

Hence the phenomenon of nobles living in genteel poverty, who were far poorer than many commoners – and these nobles tended to be the most insistent on maintaining the privileges of the nobility. For example, the noblesse d’epee in the ancien regime were the most conservative of the Second Estate, resistant to both the rising bourgeoise and the noblesse de robe (who they saw as upjumped commoners and not true nobles).
As for the Templetons, we don’t really know why, any more than we know why the Tallharts or the Glovers are Masterly Houses despite the fact that the Glovers were once a royal house.