Laptop powerbank, AC current
What you want is like a UPS. Computer UPS'es are optimized for a few minutes runtime at high power, which doesn't fit your needs. A battery and an inverter would be better.

However, this is not an efficient solution, as the energy stored in the battery will go through a DC-AC conversion in the UPS, then another AC-DC conversion in the laptop's power brick. 

I'll use 85% efficiency for the power brick, although it will vary with load and adapter.

Inverter efficiency is more complicated. Oldskool transformer-based ones will have terrible efficiency (like 50%) at low loads (say, a 60W laptop on a 500VA UPS). More modern ones will fare a lot better, like 90%. If your laptop draws 100W max, pick a 200VA inverter, not a 1kVA one, to make sure it doesn't run outside of its best efficiency range.

So you can expect a global efficiency of around 75% if the inverter is good. This means 25% of battery energy will be wasted, so you'll need a larger battery.

If you power your 12V inverter from a lithium 12V battery pack which has an internal DC-DC to output a constant 12V, then this converter will also have losses. In this case you have 3 converters in series... quite the kludge.

Simpler solutions would be:


Car laptop adapter powered by 12V battery.
6S Lithium pack with a 19V buck converter (if your laptop uses 19V).
12V battery connected to laptop, if laptop accepts 12V.