Well that's a great question.
For starters, it really depends actually. For instance, obese people are going to have to lose muscle to get back to a 'normal' weight. Reason being; even though obese people generally lead sedentary lifestyles... as they gain weight, a fraction of each pound gained is actually lean body mass.
So it's obvious that an obese individual is going to have to lose some of everything.
Things change at the opposite end of the spectrum though. When you're someone who has a relatively small amount of fat to lose, things change in your body. Your body is more susceptible to burning a higher ratio of muscle to fat. It has a lot to do with survival instincts genetically wired into us from back in the cavemen days. With this in mind, losing more muscle than fat usually leaves people unhappy with the results. They're left lighter, but still soft looking and more often than not, this is not the 'look' most are going for.
In this latter case, weight training is one of the primary things you can do to 'persuade' your body to maintain the good stuff and shed the unwanted stuff.
That's the two opposite ends of the spectrum and there's a lot of stuff in the middle too.
No matter where you are, never do you HAVE to lift weights. If you want to optimize your body composition, improve strength, combat osteoporosis, etc... it's probably a good idea.
If you're simply after a particular number on the scale and don't so much worry about how you look... than you certainly don't need to lift weights.
Does that answer your question?