I don't know about specifics in terms of your laptop or whatever, but I do know a little about electrics.
If your laptop battery is @ 20v, and you plug in a 19v battery, your laptop battery will try to charge the lower voltage battery as electricity tries to create an equal charge everywhere in a circuit. If both batteries were the same size, in theory they would both end up 19.5v.
I suspect though a laptop will have some diodes or something to prevent this, but either way it wouldn't charge.
If your laptop battery died, and was reading eg 17v, then the 19v battery could charge it up a little. You would need to have some sort of regulator in there to limit the amount of current flowing to the battery though, A simple resistor would do the job, but without knowing specifics I couldn't say what size.
So it's a kind of yes and no....
Surely a better option would be a few spare batteries?
I don't recommend to replace the adapter with a battery. The charging circuit who deliver the voltage to the motherboard is expecting 20 volts continuously. The voltage from the 19V battery will drop slowly, the charging circuit is not designed for that.
Hi, @djjag1, FYI the battery is not removable in the Lenovo U310, so a spare battery is not an option to travel with it. The battery have 11.1 volts, so it's not @20V, your deduction for charging the battery don't apply for a laptop. Like you said you don't know about specifics about laptop. Best regards.