It's Not Just that Clement Doesn't Explicitly Secret Mark; Clement Has a Different Version of the Johannine Raising of Lazarus Narrative

This never gets said often enough.  Clement seems to have had a different version of the Gospel of John which resembled in many ways the Acts of John.  As I have noted many times, the Acts of John has a strange story which immediately follows the Lazarus and Dives narrative where Jesus raises the 'rich youth' in front of people to confirm what happened in the underworld.  Clement of Alexandria similarly does reference something like the 'raising of Lazarus' narrative but with considerably different words and terminology from what appears in John chapter 11.  We hear Clement declare:

And to the dead Lazarus, he said 'go forth' (ἔξιθι) and the dead man issued from his coffin (σοροῦ) such as he was before suffering (παθεῖν), having undergone resurrection.

Καὶ τῷ τεθνεῶτι Λάζαρε, εἶπεν, ἔξιθι ὃ δὲ ἐξῆλθεν τῆς σοροῦ, ὁ νεκρός, οἷος ἦν πρὶν ἢ παθεῖν, μελετήσας τὴν ἀνάστασιν.

While John 11:43, like Secret Mark only references a 'tomb' (μνημείῳ) like Secret Mark and phrases Jesus's command to Lazarus differently:

καὶ ταῦτα εἶπων φωνῇ μεγάλῃ ἐκραύγασεν· Λάζαρε, δεῦρο ἔξω.

I don't know how people simply assume that Clement is simply citing from our John. There is too much different about this narrative to allow for its uncritical acceptance.

Yes to be sure there is someone named 'Lazarus' who is dead who is ultimately resurrected by Jesus. That much is similar. However the word issued to the dead Lazarus are different. In Clement's source Jesus declares ἔξιθι; in the canonical gospel of John we read "Λάζαρε, δεῦρο ἔξω." Moreover the dead man in John is raised from a tomb (μνημείῳ) in John and Secret Mark. In Clement's source Lazarus is raised from a coffin (σοροῦ) after a prolonged 'suffering' (παθεῖν). The resemblance here at least seems far closer to the unnamed neaniskos in Luke chapter 7:12 - 14:

Now when he drew near to the gate of the city, behold, one who was dead was carried out, the onlyborn son (μονογενὴς) of his mother, and she was a widow. Many people of the city were with her. And when the Lord saw her, he had compassion on her, and said to her, 'Weep not.' And He came up and touched the coffin (σοροῦ); and the bearers came to a halt. And He said, "Young man, I say to you, arise! (νεανίσκε, σοὶ λέγω, ἐγέρθητι)

I am one of many scholars who suspects that there was a lost original 'Gospel of John' which differed greatly from our canonical text, and which probably included synoptic material (i.e. a Diatessaron).  What this text looked like exactly is difficult to say.  But Clement is clearly not citing from our canonical gospel of John here. That much is for sure.