The late Sheldon Brown shifted his Sturmey Archer 3-speed hubs with a DT friction shifter for years and reported no problems.

Now, and this is important, you gotta line up 2nd gear accurately. If you don't get 2nd lined up, your hub can have a short and very unhappy life.

The Shimano 3-speed bell crank has an indicator on it for 2nd gear alignment, and the Sturmey hubs have a shoulder that lines up with the end of the axle. With your friction shifter, you have to know ~somehow~ when the shifter is in the right position to align 2nd gear. Mr. Brown said on his set-up that it was when the shifter pointed at his navel.

Of course the other two gears are found on the shifter at cable slack and cable taut.

Besides friction shifters, another approach with a three-speed is to use a many-speeds indexed shifter (DT, bar end or brifter) and set one of the middle index positions to 2nd gear. This acurate shifter index position can be found when riding by counting clicks, visual observation, looking at the shifter's indicator (were applicable) or feel.

At a cycle swap meet I picked up an old Shimano LH (front) bar end shifter that had a single index click position in the middle of its travel. It's perfect for three-speed hub 2nd gear shift position.