Pick through and wash the lima beans. Put them into a heavy pot and add enough cold water to cover by 2 inches. Bring to a boil and then simmer, partially covered, until they are very tender but not mushy. Remove from the heat and drain, reserving the cooking liquid.
To the bowl of a food processor fitted with a steal blade, add the drained beans, garlic, tahini, salt, pepper, and cayenne. Puree this mixture, and with the motor running, slowly pour in the olive oil and lemon juice.
If the puree is too thick, pour in a little of the reserved cooking liquid until the puree is silky smooth in appearance and on the tongue. Taste carefully for seasoning and add more salt and cayenne, if desired.
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