Power in = power out. I'm no EE, but I would imagine that the electrical consumption when charging is identical to any other battery. Unless there is some charger efficiency that is better with the lithium, but I doubt that.
The rest of the conversation is interesting. For somewhere between 4 and 5 times the cost of a conventional AGM 4 battery setup, you save 200-250lbs of weight. In my experience, the conventional batteries will last between 3-5 years if properly maintained. Assuming they only last 3 years, and the most expensive batteries are still 4 times cheaper than lithium, it still makes sense to go conventional. I can have 12 years of reliable conventional batteries for the same money, for the cost of 200+ lbs in my boat. 2 more years of batteries by my assumptions is worth $883.00. Is it worth $883.00 for 200+ lbs of wieght reduction? To some it will be. For most though, the extra upfront money combined with the skepticism over the 10 year life will have people in the wait and see category. Once this option is deemed reliable and only 3 times more expensive than traditional, it will be a no brainier.
(Assumptions: AGM 4 battery set is between $1000-$1350 and lasts 3 years minimum, comparable lithium set is 5600 and lasts 10 years minimum)