Johnson traveled extensively during his presidency, but almost all of it was domestically. He made only one official State Visit during his entire presidency, in 1966 to Asia:
https://en.wikipedia.org/wiki/List_of_international_trips_made_by_the_President_of_the_United_States#Lyndon_B._Johnson
His only overnight trip to Europe was unscheduled: to Germany for Konrad Adenauer's funeral, which the Queen did not attend.
Johnson also had Vietnam/Civil Rights to contend with; the Queen had Rhodesia and the EEC. The EEC is a circumstance that one could easily speculate that kept the Queen and the President apart as well. The United Kingdom's attempts to join the EEC were repeatedly contested by DeGaulle, who viewed the U.K. as being too much controlled by the United States. So official state visits between the the U.S. and U.K. would not have been a wise EEC-relations move at the time for the U.K., especially when one also considers Continental Europe's opinion of U.S. involvement in Vietnam.
Johnson did meet officially and privately with Prime Ministers Douglas-Home and Wilson on several occasions during his incumbency.
Note: The Queen met Gerald Ford only during the Bicentennial celebration in 1976 when she visited the U.S. He did not visit England during his presidency.
I believe he is the only other President that she did not "host." But they partied big-time in the U.S.!
http://www.speedace.info/speedace_images/queen_elizabeth_president_ford_usa.jpg