Levant Digital Marketing is a company which does Search Engine Optimization in the Middle East. They seem to be a very new company (the domain was registered in January of 2011). They are part of "JHG Holding", but this itself is also only from 2009 (and their site contains minimal content). I didn't manage to find their headquarters on Google Maps either (but this might just be an issue with Google Maps in foreign countries). Their phone number is indeed from Lebanon (as their physical address is). Their facebook page is non-existent at the moment (was it deleted?) and the twitter account is completely empty.
All in all, while I couln't find anything explicitly negative about them, it is more the case that I couldn't find anything concrete about them :-). As far as advice goes, when starting out you are better off with some simple steps, and when you grow you might consider looking into a SEO consultancy, but take care to find a reputable one rather than a cheap one or one which promises you the moon.
Full disclosure: this is a paid review from ReviewMe. Under the terms of the understanding I was not obligated to skew my viewpoint in any way (ie. only post positive facts).