Safely powering Dell laptop from external Li-ion battery with a 11.1V/19.5V step-up converter
Since you have 12 Li-Ion cells, instead going the complicated and less efficient route, I would use 5 cells in series instead, which would provide anywhere from around 18V to 21V, and this should be tolerable by most, if not all, laptops with a 19V-rated input.
With 5 cells in series, their load current will be almost cut in half because the laptop's DC-DC converter(s) will pull the watts needed, and because there will be no loss from the boost converter (about 10% or so).
You could make 2 strings of 5 cells in series and connect them together in parallel so that they last longer, or your could leave them separate so that you charge one while the other one is being used.