The Libertarian Party may have presidential primaries in as many as sixteen jurisdictions in 2020, which would be more than any party (other than the Democratic and Republican Parties) has ever had. In a few states in the past, though, state Libertarian Parties have declined to have presidential primaries even though they were entitled to them, so it isn’t possible to know now how many Libertarian presidential primaries there will be.
It appears that there could be Libertarian 2020 presidential primaries in Arizona, California, Delaware (although ballot access for candidates is difficult), D.C., Idaho, Massachusetts, Missouri, Montana, Nebraska, New York, North Carolina, Ohio, Oklahoma, South Dakota, and Utah. There is a possibility of one in New Mexico also, if the state agrees that the party is still entitled to a primary. The New Mexico Secretary of State still lists the Libertarian Party in its voter registration statistics. New Mexico also keeps track of the number of registrants in qualified minor parties, but does not display that data on its web page, so the fact that the Secretary has the Libertarian Party in its chart implies that the party is still considered a party entitled to a primary.