Cut away any excess fat from the chicken and pour the juice of the lemon all over it. Season with salt.
Heat enough vegetable oil in a medium sized frying pan so that there is approximately 1/4 inch oil in the pan.
Once the oil is hot reduce heat to medium and add the chicken pieces; you will likely have to do this in batches so that you don't overcrowd the pan.
Fry the chicken until golden brown, approximately 5 minutes per side.
Remove the chicken from the frying pan and set aside.
Season the chicken with pepper.
Fry the potatoes in the same oil and pan that you used to fry the chicken. Fry for approximately 5 - 7 minutes, turning occasionally, until the potatoes have started to brown.
As the potatoes are ready, remove them from the pan and set aside.