Three things should be clear:
1. Trump's fantasy that he lost the popular vote due to voter fraud is just that.
2. An investigation into voter fraud by the Trump administration, especially one by Sessions-led DOJ, cannot be trusted.
3. A fraudulent investigation report that has not been pre-emptively or simultaneously met by independent investigations, and that legitimizes Trump's fantasy, would be an unmitigated disaster for democracy in the US.
To prevent the disaster in 3., a fund, or multiple funds, should be established by universities and private foundations to support multiple independent investigations for whatever Trump orders investigations for. I say multiple because Trump's admin. can be expected to give the results an "alternative facts" spin, which looks more ridiculous the more investigations there are. Let them offer to do it for Trump first, and then do it independently when he refuses. Let them have all the transparencies and checks that Trump investigations will not. Let them include scientists and researchers from multiple points on the ideological spectrum. Just don't let them be tied to the Trump administration in any way, shape, or form.
Point 1. is clear because there has already been research done and it indicates that voter fraud is rare. Even the highest estimates of fraud do not come close to justifying Trump's wild speculations. There is also no independent reason to believe that whatever fraudulent votes there were in the election favored Clinton by that wide of a margin.
Point 2. is clear because Trump himself repeatedly lies, and everybody has already seen that he sends his representatives out to lie to the American people. His administration betrayed the trust of all Americans from Day 1 and cannot be relied on to tell the truth. Period. Further, Trump lives by a tribalistic/Mafioso ethic of loyalty and vengeance. Sessions was Trump's earliest and most loyal defender, and has been duly rewarded. For Sessions to deliver anything other than a confirmation of Trump's fantasy would be a betrayal of the loyalty pact they have now consummated.
The way the investigation has been pitched so far is also unacceptable and indicates intended mischief. There has been talk of the investigation only targeting "big states", which is completely arbitrary. Even if there were some antecedent reason to think that fraud only occurs in "big states" it must ultimately be treated as an empirical hypothesis that cannot be tested if "small states" are left out of the investigation.
Finally, there is actual evidence and reason to think that voter suppression could have influenced the vote tallies in places like Wisconsin and North Carolina. If we are going to have a comprehensive investigation into mischievous influence on vote totals, investigating the effects of voter suppression must be a part of that. Truly principled conservatives should agree. If anything, government should facilitate voting. But the history of government regulation of voting is a history of restricting and suppressing the voting rights of particular groups in society. If this is genuinely a non-partisan issue for conservatives, they should be fully onboard with investigating whether and how current government regulations limit the abilities of people to exercise their voting rights.
Point 3. is clear because fraudulently legitimating this delusion of Trump's would genuinely put the USA deeply into Orwellian 1984 territory. It would provide conservative states all the justification they need to put even more restrictive regulations on voting rights. And the Trump admin. would employ intimidation tactics in an effort to force more liberal states to do the same. All of this together would more deeply divide the nation, possibly to the point of political violence.
Doesn't this reward Trump's childish behavior? Can we really expect investigators to hunt down every crazy claim Trump thinks should be investigated? Almost certainly no, to the first question. The results of a truly independent and thorough investigation are certain to disprove Trump's delusions, even if they turned up a little more fraud than previous investigations have. It would make the still sane, rational people in his administration discourage him from trying again. And when he nevertheless does try again, because he has that little self-control, he may be so discredited that it may not matter. Besides, 4 years (or less) of this is worth it to prevent disaster. Trust me, there are enough researchers, statisticians, and scientists out there who could and would love to take an outrageous Trumpism and use it for fodder to fund a legitimate investigation into something worthwhile.
To say more of what I envision: the fund or granting organization should be governed by a team of scientists/statisticians/researchers (SSR's), preferably well established ones (perhaps emeritus or close to retirement who are willing to volunteer some time) with well regarded records of work. For this particular (voting) investigation, assemble a team of political scientists, sociologists, statisticians, etc. to establish (and publish) a set of objectives for the investigation, and methods for achieving them. A team of SSR's with diverse ideological backgrounds should be found, though quality of past work should not be sacrificed to include every one who thinks they should be on it. This may inevitably cause some to denounce the investigation and say that they were locked out for no good reason. That's, like I said, inevitable, and what's more important is that there be a good deal of transparency, which will certainly be more than whatever the Trump team goes ahead with. Then let them hire fledgling SSR's to carry out the investigation.
Unfortunately, I don't have the kind of influence necessary to get something like this going. But I'm putting it out there anyway, believing that there is a minuscule chance that someone who does will see it and act. This investigation is the first major battle in the war against Trump's Orwellian nightmare and we, the American people, cannot afford not to have an army of our own.