Interesting info on where "hawk a loogie" might come from, which answers the original question as well I think.
To hawk a loogie is a slang phrase meaning to expectorate a glob of phlegm from the back of the throat. It comes in many variants. Hawk is often hock or hang, and loogie can be looey, louie, or lunger. The phrase is the coming together of two words, one quite old and the other rather new.
The old one is hawk or hock. It’s probably echoic in origin and dates to the late sixteenth century. From Richard Mulcaster’s 1581 treatise on education, Positions, which also contains medical advice relevant to bringing up young boys:
Of all these diuersities in walking the moderate is most profitable, which alone of all, that I rekened, hath no point either of to much, or of to litle, and yet it is both much, and strayning, which be the two properties of an healthfull walke. It is good for the head, the eyes, the throte, the chest, when they be out of frame: so the partie spit not blood. For distilling from the head, for difficultie of breath, for a moyste and and pained stomacke, wherin the nurriture either groweth bitter or corrupteth: for the iaundise, costisnesse, fleeting of the meat in the stomacke, stopping of the vrine, ache of the hippes, and generally for all such, as either neede to prouoke any superfluitie from the vpper partes downward, or to send that packing, which is already in waye to depart. Now to the contrarie it is naught for agues, bycause it encreaseth heat, and so conseque[n]tly the disease: for the falling euill, for hauking vp of blood: and in the time when one is making water.
Loogie is of more recent vintage, dating to the latter half of the twentieth century, at least in writing. It appears in Carlo Curti’s 1967 biography of movie mogul Spyros Skouros, Skouras: King of Fox Studios:
“Out kid!” he ordered as one of his bodyguards put me in an armlock. I spit a lugey on him and he slapped my face.
The phrase is recorded in student slang in the journal Current Slang from 1970:
Hang a louie, v. To spit on someone.—College students, both sexes, Minnesota.
And another example is found in Julian Moynahan’s 1979 novel Where the Land and Water Meet:
In the old neighborhood, by Raymond Street Park, to cough up and expectorate heavy phlegm from the back of the throat was to “hawk a lunger.” When you did it, the remark to make was “Go pick the bones out of that one!”
Not a very pleasant image.