Since no one else has responded, my opinion that is based completely off my personal feeling and not a single rubric (which I do not have in front of me,) would be no.

I'd say no, since there is no incense used at the gospel on Good Friday, the instance where it would be conceivably used.

The missal says:

21. [On Palm Sunday,] the narrative of the Lord’s Passion is read without candles and without incense, with no greeting or signing of the book.

[...]

9. [On Good Friday,] the narrative of the Lord’s Passion according to John (18: 1–19: 42) is read in the same way as on the preceding Sunday.

I think this points us to the fact that using incense at lauds on Good Friday, while possibly allowable, wouldn't be within the spirit of the law.

Traditionally incense was not used at the hours during the Triduum. There is no rubric that I know of (for the ordinary form) that specifically forbids it. It would be inconsistent with the rubrics of the Mass, however, as pointed out previously. The altar, being stripped of cross, candles, cloths and other ornaments is neither venerated nor incensed by the celebrant at the Solemn Liturgy on Good Friday, so it makes little sense to incense it at the Benedictus of Morning Prayer. It should be noted also that the public celebration of the Office of Readings before Morning Prayer (Lauds) is encouraged on Good Friday and Holy Saturday (cf. GILH 210, CB 296).