can Lufthansa recharge laptop in international flight

Lufthansa have power outlets only in Business and First class.

Try asking the flight attendants if you can plug your laptop into the outlet for an unoccupied seat in BC or first class so it can charge during the flight. Lufthansa tends to be "by the book" so you may be told no..

A 20-hour trip will have one or more stops or/and plane changes. You should be able to find an electrical outlet in between flights.

Do look into upgrading, at least for part of your trip. Having a ticket in BC or FC for any part of your trip should give you the opportunity to recharge your laptop in-flight. It should also give you the other BC/FC perks, like lounge access. Lounges always have electrical outlets you can use to recharge.

Lufthansa's frequent flier program only allows you to purchase 12000 miles per year, which is only enough to upgrade from EC to BC on short flights. However, United's program lets you purchase up to 50000 miles, which would be enough to upgrade (1-way) just about anywhere Lufthansa could fly you. Do the research before you buy the miles to make sure your ticket is upgradable AND there are vacant seats in BC. Lufthansa and United are partners and you can use United FF miles on Lufthansa.

The only other suggestion I can make is to take an extra battery or two if you really need to work that much while in-flight.