These are all good questions and I would bet that time will answer all for us ice fisherman. There are few things you need to keep in mind as you look at this technology though; first of all, which Lithium technology are you looking to use. As you may or may not know there are several types of Lithium compounds used in making batteries and each has its place and use. The batteries that I am using and is part of the discussion here is a Lithium Iron Phosphate compound. The battery is made by using 3 smaller cells in parallel and then 4 cell sets in series to create the 12V @ whatever amp hour configuration. You will find that these batteries operate a higher output voltage than you are used to since they charge to a maximum cutout voltage of 16.0V. The battery will operate around 12.8 – 13.2 V for a fully charged unit with the low current draw that we see in a Marcum unit. These technologies are fairly new to the public and have a tremendous sticker shock value, some of which makes the cost vary is the fact that for proper operation there is actually electronics built directly into the battery to make sure that damage does not occur if misused. If weight is a significant issue, these batteries weigh in at 2.8Lbs for a 10AH unit versus the 5.7Lbs for a 9 AH normal lead acid battery. Also, if you can believe charts, the cold temperature usage of these have been tested at -20F and have a good lasting power curve that indicates that some of the temperature issue have been fixed. As for the long life aspect of these batteries, it will totally depend on how you use it and how well you take care of it.
The battery that I use is the K2 series of batteries and charger so that is why I have included their info here. There is nothing unique about their data other than it is what I know of from my research.
If you use these batteries or not is purely a personal choice, but make sure that you do the research up front because it can be a big investment and you need to know what is the proper way to use and take care of your investment.