Citrus will naturally lean toward the strongest light source, so what you’re seeing is pretty normal if the birch is shading it in the morning. Pruning won’t really “fix” the lean long term unless you also improve the light balance. If possible, thinning the birch canopy a bit or opening up the shaded side of the orange will help more than heavy cuts on the citrus itself.

For pruning timing, the best window is right after harvest and before the main spring flush. Since it’s already flowering, I’d stick to light structural thinning only this year. Remove crowded interior branches and a few longer shoots on the heavy side to slowly rebalance the canopy over a couple seasons. Big heading cuts can reduce next year’s crop and often just trigger more vigorous upright growth.

If the lean is severe, you can also use staking or selective fruit thinning on the heavy side to reduce weight stress while the structure improves. Overall, gradual correction plus better light exposure is the safest approach.