The usual account runs in a straight line. Juliana, an Augustinian canoness at Mont Cornillon near Liege, sees repeatedly from her youth a full moon with a dark band across it and comes to read it as the church's year lacking a feast of the sacrament. She persuades the local clergy; the bishop of Liege institutes it in 1246. One of those clergy, Jacques Pantaleon, later becomes Urban IV, and in 1264 he extends the feast to the entire Latin church by the bull Transiturus de hoc mundo, the first universal feast a pope ever mandated. He commissions Thomas Aquinas to write the office, and Aquinas produces Pange lingua, Lauda Sion, Verbum supernum and Adoro te devote.
Most of this holds. The Liege institution of 1246 is documented, Transiturus is dated 1264, and the Aquinas attribution, doubted through much of the twentieth century, has been substantially rehabilitated, with two office settings now generally accepted as his.
Where it strains is the causal chain. Surviving office material from Liege points to a liturgy already composed and circulating in its own right, which complicates the picture of a papal feast simply fulfilling a local visionary's request eighteen years later. Eucharistic devotion was intensifying across the thirteenth century for reasons independent of any one person: the doctrine of transubstantiation had been affirmed at the Fourth Lateran Council in 1215, and the elevation of the host at Mass, the practice that made the sacrament something to look at, spread through the same decades.
Juliana's role is real. Reading it as the single cause of the feast tells a story with one protagonist about something that had many.