The three-letter word for a work unit is "erg".
A three-letter word that means "exist" is almost always "are." See if it will work.
work
"BOSS"
oeuvre
Immigrate...
erg
A three-letter word for 'lucrative' is 'pay', as in, 'Does his work pay well? which could also be expressed as, 'Is his work lucrative?'
Joules-the unit of work
A three-letter word that means "exist" is almost always "are." See if it will work.
A three-letter word that means "exist" is almost always "are." See if it will work.
There are 9 * 8 * 7, or 504, three letter permutations that can be made from the letters in the work CLIPBOARD.
con
erg
Word.
It appears you are looking for CON to make conduct and consign, but contense is not a word. The only three-letter combination you can use in front of TENSE is pretense, which does not work with the other two words. However, if you replace TENSE with DENSE, your question would work.
work
An eight-letter word cannot be made from four letters. T, I, E and S are not sufficient to make an eight-letter word without knowing what letters can be repeated and how often they are repeated. TESTIEST could work if you allow three Ts.