Is ghusl required after the discharge of semen that is dispersed over widely spaced times, if its first discharge occurred after the transfer of semen without ejaculation, and the second and third discharges of semen were without lust, with doubt as to whether it was for the same reason or due to a new lust because of obsessive thoughts?

You made a mistake by responding to the whispers of doubt (waswās), and the duty was to ignore them. If you performed ghusl for the emission of semen, that suffices you, and ghusl is not obligatory for any semen that exits afterward, because it is a remnant of the first semen, and no new pleasure necessitating its expulsion occurred. You must ignore these whispers, as giving in to them leads to great evil.