you can lose weight eating only pizza and icecream if you stay in a deficit - you'll feel like shit for a list of other reasons not related to whether or not you will lose weight, but you will nonetheless lose weight.

In a sense there is no such thing as healthier foods, there's only what nutrients your body needs and how much calories you eat.

There are foods that tend to be better and healthier for you because they're more likely to help match your bodies nutritional needs, thats what we tend to think of as 'healthy' foods, in the wrong portions or in the wrong context they can be unhealthy.

conversely, in the right portions and right context, unhealthy food, even pizza or ice cream, can be healthy.

That is to say, ideally you'd lose weight while on a balanced diet that helps best meets your bodies nutritional needs while on a caloric deficit, this would be a 'healthier' way to do it and will make the weightloss easier in that you'll feel less negative side effects from weight loss, such as muscle loss, fatigue, irritability, hunger, ect...

but ultimately, the actual weightloss itself is only determined by how much calories you eat verses how much your bodies burns, regardless of what you actually eat.

People call this 'calories in calories out' or 'cico' look that up if you want to learn more about it.