Yes, but not in the way most marketers think when they ask this question.  Facebook carefully protects user data including names, emails, likes, friend lists, and more.  This data is proprietary to Facebook and can’t be removed from the platform.  Thus, Lytics cannot tell you “which of my audience likes my page” and any other Facebook-proprietary data.

What some savvy marketers are doing is to make use of referrals and link clicks from Facebook to their site and tracking those users as “social.”  Some clients make use of the campaign parameters that Lytics natively tracks to define who has come from certain content and are serving personalized messaging to them.

Similarly, social sign-on data can have some limited data from Facebook if the user has authenticated with Facebook when signing in to your site or app.  However, we’re limited their by what the social sign-on provider collects on behalf of the client -- usually a name and email address.  We have commonly-used integrations with Gigya and Janrain for this type of information.  We also have seen some clients have success building their own integration to Facebook social sign-on.  Help can be found here:
https://developers.facebook.com/docs/facebook-login/best-practices

Of course, you can make use of any data you’ve collected for powerful ad targeting in Facebook via our API-based connections for targeting of anonymous users or know users for whom you have an email address.