Which one is correct:
(a)Lots of Diamonds.
(b)Lot of Diamonds.
(c)Lots of Diamond.
Is there any rule.
Yes, there is a rule.
Both 'a lot of' and 'lots of' can be used with either countable or uncountable nouns; the countables then assume the plural form, uncountables remain singular.
We've eaten all our pears but we still have got a lot of / lots of apples.
Be prepared to see a lot of / lots of snow if you're going there in the winter.
'diamond' is a countable noun, therefore 'a lot of / lots of diamonds' is correct.
Please notice that the word 'lot' is a countable noun in this expression, and so it requires an indefinite article with its singular form.
Hope this helps.