My best guess is that the tune for the Te Lucis is in the left hand, and that it doesn't match any of the melodies in the Liber -- and there is not a shortage of reasons why this might be the case.
The only connexion of this verset to Te Lucis would be the title and the mode, and the fact that the opening interval of a rising major 3rd occurs in de Cabezon's verset and the mode viii melody found on p. 266 of LU. (This is also the tune used in Mr Hawkins's example below here.) Otherwise, there is no trace of a cantus firmus, plain or decorated. The only determining factor in choosing which of the several melodies associated with Te Lucis and de Cabezon's verset would be modal agreement. Beyond the opening major 3rd of de Cabezon's verset and that of the mode viii melody there is no correspondence other than modal of the verset to the chant melody.
One often finds one or two or more versets such as this based on hymn or other tunes, but not being sufficient in number to be used alternatim-wise with multiple verses or stanzas (Buxheimer Orgelbuch, Tallis, Frescobaldi, Scheidemann, et al.). How, or in what context, they were intended to be played is an unanswered question. It could be that, like the English In nomines and Gloria tibi trinitases, etc., they were 'stand alone' pieces meant solely for private pleasure, or were exemplars for students.
The primary reason (and this can be a problem for polyphonic alternatim works by Morales and Victoria, too) is that Spain did/does not use use Gregorian Chant, which is proper to Rome, but Mozarabic Chant, which is proper to the Mozarabic Rite of Spain.
Prior to the imposition of the Missal of the Roman Curia on the Western Church after the Council of Trent, many places in the west had their own Usages, which included proper chants, some are similar to the Roman/Gregorian melodies, others are completely different. So, Milan has the Ambrosian Rite with its Ambrosian Chant; most of England had the Sarum (Salisbury) Use with its Sarum Chant; Spain had the Mozarabic Rite, though it died much sooner than Trent, though the Mozarabic Chant tradition remained; Paris had its Use and Chant, etc.
I believe, though, Salieri, that the melodies of the various local usages and rites differed more as variants of essentially the same melody - not being totally different melodies. For instance, Sarum 'O' antiphons begin with a minor third rather than the Roman perfect fourth, but, otherwise, matched the Roman version. Sarum hymn tunes tended to be more or somewhat more elaborate variants of their Roman counterparts. The same is basically true of all the non-Roman chant. Of course, there were instances of totally different tunes at certain locations, but, as a rule, the differences had to do with greater or lesser elaboration of the same basic melody.
Most here will know that the same dynamic typified the various Protestant gesangbuchs, whose tunes were very often variations of one another from town to town - much as the difference we have discussed on another recent thread about Grosser Gott and those who sing the ornamental eighth notes and repeat the last two lines, and those who don't.
I do know that the Spanish music dudes and communities had their own local versions of many popular texts. There are dozens of settings of the Pange Lingua by conposers such as Bruno and others that use a tune to that text that was very popular but does not exist in any litugical books.
Thanks for the responses. I tried to combine the tune with the text in a video, since we don't know how the text was sung I thought just having it read would be better than nothing: https://www.youtube.com/watch?v=xTWA6Js17WI
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