For a long distance (many nights) along the trail I think AA’s lights are the way to go. AA batteries can be purchased just about anywhere in the US.
Take a look at the Skilhunt H15 AA powered headlamp, there is (was) a group buy going on.
An alternative is the Fenix HL50 which puns on one AA or one CR123.
There are many AA light to chose.
I am envious for your friend to hike the PCT
A Li-ion rechargeable will need to be recharged obviously, which the hiker needs to bring a charger (extra weight, or light with built in charger) and then have power source to recharge, recharging takes hours which would mean a stop over somewhere during the hike (extra time).
The downside with AA’s is that carrying batteries do add weight.