Lanais have a sloped floor to allow for drainage, so if you are completely enclosing your lanai, you will probably want the floor to be level. Also, there may also be some concerns about the stress cuts. If you get a crack in the original slab, it will probably propagate to the new slab, but in an irregular pattern. I would get a few estimates on doing this, as you do not want to do it a second time.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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