Never before has any party, other than the Republican and Democratic Parties, been entitled to presidential primaries in as many as ten states in any one year. But it is possible in 2020 the Libertarian Party might have presidential primaries in as many as 20 states, if it wants them.
It is very likely that the party will be entitled to its own presidential primary in 2020 in Arizona, California, Idaho, Missouri, Montana, Nebraska, North Carolina, Oklahoma, and South Dakota.
It is likely that it will have presidential primaries in the District of Columbia and Massachusetts. It all depends on whether the party gets as many as 7,500 votes in D.C. for any partisan district race, and whether it gets 3% for Massachusetts Auditor.
It is possible that the party will be entitled to presidential primaries in Arkansas, Delaware, Illinois, Michigan, New Hampshire, New Mexico, New York, North Dakota, and Ohio, depending on how well the party does in the 2018 election. In Delaware, the variable has nothing to do with votes. Qualified parties are entitled to their own presidential primary in Delaware (even though they nominate by convention for other office). But no qualified third party in Delaware ever has a presidential primary because it is so difficult for candidates to get on the presidential primary of a small party. Generally they don’t have enough registered voters for a candidate to get 500 signatures of party members. Furthermore, at least two candidates must petition, for the state to hold a presidential primary.
Libertarian presidential primaries are never binding, but if the presidential nomination is hotly contested in 2020 (and it probably will be), the candidate who wins most of the presidential primaries will probably have a psychological edge.