I would say that yes, in the second sentence, the present tense travaille, was chosen for its stylistic impact, bringing a sense of immediacy to the narration. So yes, that travaille would be the key to making this sentence interesting (it is, IMHO, a good, pleasant style).

I think “weird” is not the right word here. It’s just different styles, the second one probably being more “modern” (not implying common) than Gide’s style. My feeling is that writers before the fifties probably would not have considered using this present tense style (I could be wrong).

I was writing about the Gide sentence explaining why it makes sense, but I realize it’s not the point, the real problem is with the second one.

It feels weird of the combo “deux ans” + “lorsque“. The suddennes of “lorsque” doesn’t match very well with the long duration of two years. It’s like saying “I was doing something for 2 years then suddenly I found a solution”.

You can say :

Je mange mon sandwich sans faire attention aux gens autour de moi lorsqu’un inconnu vient m’approcher.

The tenses are the same, it also uses lorsque, but the implication are different. Eating a sandwich is a somewhat short action, it makes sense to be interrupted.

Also, “Je travaille sur un projet depuis deux ans” doesn’t sound like narration present, it sounds like general truth present, just like saying “je travaille dans l’immobilier“. And you cannot use “lorsque” in a sentence using general truth present, it just doesn’t make sense.

In your sentence, I understand that finding the solution marked the end of the project, that’s an important component. Using “depuis” with present means you’re still doing the action (pendant often means it’s over, but not necessarily). You can use present for narration but still use past for stuff that already happened at the time of the story.

Narration present is more about describing short actions. You can describe long actions (more than a day I mean), but it sounds weird to interrupt them with a short sentence.

You could say :

Je travaille sur ce projet pendant 2 ans. Un jour, je trouve la solution.

or

Je commence à travailler sur ce projet. Deux ans plus tard/Après deux ans, je trouve la solution.

(If those two sentences raise more questions, please ask them in comment as they come.)