The ensuing success of the Turks perhaps would have made it a moot point in any case, but looking at the Treaty of Sevres, while it does make mention of the Kurds, Articles 62,63, and 64 seem fairly weak compared to the strength of Article 88 recognizing Armenia. It basically is just "If the Kurds can get their shit together, maybe something will happen"?
Even aside from the eventual failure of Sevres though, there seems to have been no referendum held as laid out - which would have been done well before Lausanne - and in any case, even if Turkey abrogated, the theoretical Kurdistan also included parts of Iraq, which could have been moved forward on.
So why was there what appears to be so little interest in the Kurds at the time, and failure to follow through with what marginal promises were nevertheless made?
You may be interested in a long, three part answer:
Parts II and III talk a lot about the treaty of Sevres and its aftermath.
I talk a little more about the issue of tribalism, mentioned by /u/medium_well_soyuz_1, here.
Obviously, this was a tumultuous period of history for the whole of the Middle East. The Ottoman Empire had basically been the power in the region since 1453, and now was gone (even if the Ottomans had been on a steady decline throughout the preceding century or more). Mandates were created and held by Britain and France. For the most part, these were created from old Ottoman provinces. Now, however they had to build nations from scratch and so this was a period of intense nationalism for many nations.
Turkey, in particular, was an example of this nation-building. Atatürk promulgated the Six Arrows, which included an adherence to secularism and the nation, neither of which meshed with Kurdish identity. Kurds identified as Kurds not Turks, which is divisive if you are forming a nation based on the premise that everyone is a Turk. Unsurprisingly, the Kurds actually did rise up in Turkey in 1925. William Cleveland calls this uprising, "a mix of Kurdish nationalism and Islamic revivalism." Both of these were dangerous to Atatürk, who crushed the rebellion and executed its leaders.
Iraq is another interesting example. Basically, Iraq was built from three Ottoman provinces, Basra, Baghdad, and Mosul. The South was largely Shi'a Muslim, Central Iraq was largely Sunni Muslim, and Northern Iraq was the most sizable Kurdish population. Kurds typically identify as Sunni, but not always. Anyway, they faced many of he same problems in the fledgling Iraq as their compatriots in Turkey did. A new nation was created, and the monarch needed stability and obedience. Ultimately, the Kurds rose up as they felt the British were not protecting their sovereignty, and were crushed. If I'm not mistaken, it's the first RAF bombing in the Middle East. The Kurds laid claim to Kirkuk, which was, and still is, a massive oil producing area.
So why did the Kurds fail to form a state? One reason is their largely tribal society. The Kurds were not a monolith. One of the major reasons a referendum never came about was that the Kurds could not agree on the extent of their territory. They claimed lands in Turkey that the British has no authority to give them. Another that we can plainly see here is a lack of Western support. Nations like Israel and Iraq received huge support from Britain. The Kurds never received this sort of assistance.
Finally, as to your point about Armenia, Armenia was specifically mentioned because it had been declared. While the borders needed adjusting, there was a very very brief Armenian republic until the Turks and Soviets conquered it. That's why it is more clearly defined. It already existed in some form before the Treaty of Sevres.
Source: William Cleveland, A History of the Modern Middle East