I have always mixed the grapefruit juice with olive oil. I usually used freshly squeezed grapefruit juice, but once I used grapefruit juice out of the bottle. I would use half grapefruit juice and half olive oil (1/2 cup of each)
I also would usually squeeze the juice of a lemon with the mixture and also add lemon juice to the Epsom Salt mixture.
I never used lime juice, so I can't compare it. I can only say grapefruit juice works fine.