Unfortunately the pin naming is a bit confusing. The other pin will have 5v on it when USB is connected, so you definitely don't want to put the lithium battery on that :)
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It's the Pin 1 -
BAT_IN
on this diagram (your second choice): http://www.espruino.com/Pico#pinoutUnfortunately the pin naming is a bit confusing. The other pin will have 5v on it when USB is connected, so you definitely don't want to put the lithium battery on that :)