I used to believe this (as did many people) but no longer do. The amount of extra calories burned with a higher muscle mass is just not significant enough to make this a relevant idea.

Of course, there are many, many other reasons to lift weights. Health and longevity aside, the reason most people want to lose weight is to look better - so what they should really aim for isn't to lose weight, it's to lose fat and increase muscle mass. For that, you need both a caloric deficit and weight lifting.