Unfortunately, as far as I know, there are no chant settings of the (eight?) different Lenten Gospel Acclamation antiphons. I’ve looked all over the place for exactly what you’ve described.

If I remember correctly, there may be a setting of a different text set as a Lenten Gospel Acc in Liber Cantualis, and maybe yet another in the Parish Book of Chant. But I don’t think there’s an official version of “Laus tibi” or the others published anywhere by Solesmes. I think I also looked up at one point each of the gospel acclamation texts in the Hesbert Corpus Antiphonali Officium if there were any matches but had no luck.

For parish use, I’d recommend pointing it to a psalm tone, or using/adapting one of the simple tracts in the Graduale Simplex (under any Lenten Mass chant called “psalmus responsorius ii” or the “tractus”, such as pages 84-85). There may be another option in the “Jubilate Deo” Editio Vaticana booklet, too!

In "Singing the Mass" (available from Solesmes’ online bookshop) there are three settings of two Lenten acclamations: Laus tibi, Christe, Rex aeternae gloriae (modes IId and VIIIg) and Gloria et laus tibi, Christe (mode IVe). See p. 41. But I wouldn't call these ‘official’ settings.

The reason that there are no ‘official’ settings of the Latin texts is, I assume, the same as the reason that there are no ‘official’ settings of the Latin responsorial psalms: the gregorian repertoire has other pieces in that place, the tracts. Just like the gradual is sung when using gregorian chant and not the psalm from the lectionary.

It is interesting to note that GS was prepared for the 1962 Missal, in accordance with the mandate in SC §117 promulgated in Dec 1963, and it was ready by April 1965. Dom Cardine seems to have been one who did not let the grass grow under his feet.
The structure of the chants beteen the readings (and there were still only two readings) is different from GR, in that the Gradual antiphon with verse, is replaced with a psalmus responsorius verse, response, verse, response,↻...; or similarly a psalmus alleluiaticus in which the response is Alleluia, ... The Alleluia is replaced, not dropped, in the Lenten season with these new Lenten Acclamations, and there are still tracts. So the instructions in that first edition say :

16 b. During seasons when the Alleluia is not used,
a psalm with a psalm verse as response, and, optionally, an antiphon as the gospel acclamation with at least one verse, are sung;
or else, a psalm without a response, that is, a tract, and, optionally, the gospel acclamation as just described.

I see already a clear shift of emphasis from Antiphons with added psalm verse(s), to psalm with psalm verse refrain(response).