No, "schon" can not be omitted here. "Wie lange lernen Sie Deutsch" would refer to any time span in the present or future that is spent studying German. That sentence would be appropriate if one wanted to know how long someone plans to study German e.g. in a curriculum or this afternoon.
Examples for that would be:
- "Ich will Europäische Kultur studieren und muss dafür auch Deutsch lernen" "Wie lange lernen Sie/ lernst du (in diesem Studiengang) Deutsch?" (refering to a possible future. The answer would include all semesters spent studying German even if the speaker allready started studying)
- "Ich schreibe morgen eine Klassenarbeit in Deutsch und muss noch lernen, bevor ich mit an den Badesee fahren kann." "Und wie lange lernst du (heute) (noch) Deustch?" (refering to an ongoing or future activity. The answer would either include the time where the activity ends or the total time spent with that activity)
The sentence as-is clearly refers to the time that was already spent learning/studying German while still learning/studying but not to the time that might still be spent. Corresponding sentences would be:
- "Ich wusste gar nicht, dass Sie so gut Deutsch sprechen. Wie lange lernen Sie schon Deutsch?" (refering to the time the person has allready spent learning German up until now. The answer must include either since when or for how long the person is studying and adding information about any plans about how long the person is still going to study are irrelevant to this question)
- "Mach doch mal eine Pause. Wie lange lernst du schon Deutsch?" (refers to the time spent on an ongoing studying session and clearly does not intent on letting it keep going on for now)
If the person is not currently studying German, the more appropriate question would be "Wie lange haben Sie schon Deutsch gelernt?", and in this case, "schon" can be omitted though it still would change the tone and some nuances that are, in my opinion, too subtle and depend on too many other factors to be pointed out here.
"Schon" makes the question be about the past, the opposite would be "noch" referring
only to the future, and with neither of them, the question is about the total time spent or in some cases about the time when the activity ends.