Lifestyle Branding - is marketing to a specific target audience around how they live or how they think of themselves. Hipsters, surfers, soccer-moms ;) - the position of a product to these people would reinforce how they perceive themselves and live their life.
I think aspirational branding is more about the interest in a product by an audience. So someone would be really interested in a product but the 'aspirational' aspect of it is usually that it is out of reach. Either only available to a certain crowd, out of their price range, or it's perceived quality and value is at the top of it's class.