Uses of the word 'lack'

PCTREE

Wong Kwong Yau asks:

Would you please tell me all the uses of the word lack (in different forms) and make a sentence for each of its uses? Is the sentence 'Many children are in lack of sleep' correct? If it is wrong, what should it be?

I'm not too happy with 'in lack of', Wong, which doesn't sound quite right to me. Lack of is fine where lack is used as a noun, so you can say, for example:'The lack of amenities in the hotel surprised all of us.''There was a general lack of enthusiasm among the trainees.'
                                        Lack may also be used as a verb:'They lacked the courage necessary to cross the fast-flowing river.''When she came to start making the cake, she discovered that she lacked half the basic ingredients.'