Indeed, Omani lemons are not lemons at all! They are dried limes and also go by the names black lime, loomi, amani and noomi basra (to name a few).
I scooped these up one day at a Middle Eastern specialty store and have been adding them to braises and rice dishes ever since. They go a long way, so one of them has enough flavor for around 3 cups of basmati rice (with which it goes especially well).
Omani lemons are used in cooking throughout the Middle East and even North India. Typically, (fresh) Omani limes are boiled in salt water and then dried in the sun. This preservation process turns them anywhere from a light tan to black in color and hollow in the center. Their flavor is tart, more like the peel than the juice, without any sweetness, and they also have an indescribable muskiness. They are fantastic as a souring agent in place of lemon juice in a sauce.
To use them, you can poke a small hole in one or two and throw them into whatever slow-cooking pot is at hand. They can also be crushed or even powdered, and they are sold whole, crushed or powdered at various ethnic grocers.