You are lucky to have a shaded garden. As Lemons and Limes are the requirement of every kitchen I suppose containers is the only way forward. Cheryl as I also have to send the sun light into funny corners I use a strategically placed looking mirror to bounce the light into corners. In nurseries I have seen these plants in heavy fruit in small pots, I don't know. Either they are cutting the root ball out of the soil when in full fruit and selling fast to gullible buyers or they are using some chemical. First is a possibility because they do the same with roses at this time of the year.
Regards,
Arif.