(1) Giuliani is maintaining that he was *prospectively* working as Trump's impeachment lawyer before there was an impeachment process; in other words, what Giuliani was doing in Ukraine is somehow related to providing a *defense for Trump* before either the House or Senate.
(2) Giuliani is a "fixer" whose job is to "solve problems" for Trump that have nothing to do with the law but rather knee-capping Trump's "enemies"—thus, an attempt to encourage probes of Clinton/Biden. In this case, Giuliani isn't acting as an attorney or doing legal work.
(3) Giuliani didn't hire an investigator—which he would've done, by the way, even if he was "just" working as an "impeachment attorney"—because he wasn't doing legal *or* criminal/extra-judicial ("fixer") work. He was, instead, conducting diplomacy for America.... illegally.
If you're trying to get people to *do things*, you want the principal's highest-ranking agent doing the work.
1) What pending legal case were you working on?
2) Why did you not hire an investigator for the case?
3) Did Trump refuse to pay an investigator?
4) If *you* were investigating, why did you ask *foreigners* to investigate?