If Oswald were to receive legal assistance , whoever Oswald retained to be his lawyer then the Attorney-client privileges would be in place and by it's very nature , the attorney-client relationship affords a distinct , invaluable right to have communications protected from compelled disclosure to any 3rd party , including business associates and competitors , government agencies and even criminal Justice authorities ! If Oswald had retained a Lawyer then it would probably have been bad for certain individuals and probably bad for the Lawyer . Then there's Ruby who wanted the Warren Commission to take him back to Washington DC so he could talk and of course the WC denied Ruby the ' Trip to talk ' !
Legal counsel could have ended the interrogations and/or at the very least kept a stenographic record of what was said.
Kept the defendant's wife from isolated protective custody and questioning.
Would have objected to Lee's unsafe public exposures and transfer and prevented, at least at that time, LHO's murder by Ruby.
A few of the many reasons LHO was denied an attorney.
IMO