From the movie Goodfellas:
Jimmy: Stupid bastard! I can't fucking believe you. Now you're going to dig the hole. I got no fucking lime.
No definition that I have checked fits here. What does he mean "I got no fucking lime"?
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Lime has this apparently undeserved reputation for destroying corpses buried in it; it turns out in real life to act as a preservative, and may have been used to prevent the messy, smelly decay (putrefaction) which would only draw attention to the remains.
 In both of these instances the effect will be to prevent putrefaction ( something that no murderer wants, especially if trying to dispose of a corpse!) and effectively ‘preserve’ the body against external decomposing agents which would have been at work if quicklime was not used.
 Quicklime does have uses for burials. In the Red Cross Emergency Relief Items Catalogue, quicklime and lime are listed as a tool for aiding in proper disposal of human remains that cannot be afforded a deep burial. However, the goal of the product is not to destroy the body but rather to prevent putrefaction that create odor, and attracts flies and animals.
In general, they discovered that the lime was highly effective in preventing decay and protecting the body, rather than destroying it.
Ultimately these two sources seem a little conflicting, but the fact remains it’s got a reputation for being useful for burials, and has sometimes been so used for innocent reasons
Lime (or quicklime) is a name for calcium oxide. It's a very caustic chemical that degrades organic tissues fairly rapidly. It's a common trope in gangster movies that a freshly-killed body is covered with quicklime during burial for two reasons:
The degradation of the organic tissues looks (at least superficially) like natural decay, making the corpse like it was killed long ago rather than recently. It's also supposedly likely to destroy fingerprints or other identifying characteristics.
Quicklime is a major ingredient in concrete, and mobsters are traditionally associated with the construction business, so it would be available to them in large quantities without it being suspicious.
More on the use of quicklime for burial at this link.
The lime part of the question has been answered.
I got no (colloquial) means "I have no" or "I don't have any".
fucking is an expletive which is unacceptable in most public situations—in so-called "white collar" workplaces, at PTA meetings, at places of worship, in public interviews on TV, and so forth. Its purpose here is to express the speaker's general displeasure with the way things are going.