In this situation can you turn right from the traffic lane you are occupying?

In the photo you have stopped before a pedestrian crossing at a junction with traffic lights; on both sides of the roadway there are signs A-7 "give way" and C-2 "turn right after the sign", and the traffic lights are showing green. From the lane you are in, you are allowed to turn right - in fact, it is the only permitted direction. The answer is: yes.

The Regulation on road signs and signals states that sign C-2 requires the driver to go in the direction shown by the arrow, that is, right after the sign, and it applies at the nearest junction. A green signal allows you to drive past the traffic lights; sign A-7 applies when the traffic lights are switched off - then, before entering the junction, you give way to vehicles on the intersecting road, but on green you simply drive on. You turn right, watching out for pedestrians on the crossing beyond the junction.

Legal basis: § 35 para. 1 point 2 and para. 2 and § 95 para. 1 point 1 of the Regulation on road signs and signals; Art. 5 para. 3 of the Road Traffic Act (Prawo o ruchu drogowym)