It's a murky point, but we can fairly ascertain the positions from the initial treaty presented in 1815, and the revisions done to it about 8 months later in 1816. Article III of the initial treaty states : "The Rajah of Nipal hereby cedes to the Honourable the East India Company in perpetuity all the under-mentioned territories, viz-

First: – The whole of the lowlands between the Rivers Kali and Rapti.

Secondly: – The whole of the low lands (with the exception of Bootwul Khass) lying between the Rapti and the Gunduck.

Third:– The whole of the lowlands between the Gunduck and Coosah, in which the authority of the British Government has been introduced, or is in actual course of introduction.

Fourth:– All the low lands between the Rivers Mitchee and the Teestah.

Fifth:– All the territories within the hills eastward of the River Mitchee including the fort and lands of Nagree and the Pass of Nagarcote leading from Morung into the hills, together with the territory lying between that pass and nagerr. The aforesaid territory shall be evacuated by the Gurkha troops within forty days from this date."

The cumulative effect of these individual sub-articles would mean that only the hills and mountains east of the Kali river and west of the Mechi river would remain in Nepal. However, there was a revision done in 1816, which returned what today constitutes as the Terai region (with the exception of the four districts returned during Jung Bahadur's premiership). The revision ensured the following:

"2. With a view to gratify the Rajah in a point which he has much at heart, the British Govt is willing to restore the Terai ceded to it by the Rajah in the Treaty, to wit, the whole Terai lands lying between the Rivers Coosa and Gunduck [nullifies Article-3 point three], such as appertained to the Rajah before the late disagreement; excepting the disputed lands in the Zillahs of Tirhoot and Sarun, and excepting such portions of territory as may occur on both sides for the purpose of settling a frontier, upon investigation by the respective commissioners; and excepting such lands as may have been given in possession to any one by the British Govt upon ascertainment of his rights subsequent to the cession of Terai to that Government. In case the Rajah is desirous of retaining the lands of such ascertained proprietors, they may be exchanged for others, and let it be clearly understood that notwithstanding the considerable extent of the lands in the Zillah of Tirhoot, which have for a long time been a subject of dispute, the settlement made in the year of 1812 of Christ, corresponding with the year 1869 of Bikramajeet, shall be taken, and everything else relinquished, that is to say, that the settlement and negotiations, such as occured at that period shall in the present case hold good and be established."

"3. The British Govt is willing likewise to restore the Terai lying between the Rivers Gunduk and Rapti, that is to say, from the River Gunduk to the western limits of the Zillah of Goruckpore, together with Bootwul and Sheeraj [nullifies Article-3 point two], such as appertained to Nipal previous to the disagreements, complete, with the exception of the disputed places in the Terai, and such quantity of ground as may be considered mutually to be requisite for the new boundary."

The revisions only deal with the southern plains, and not the hilly regions, which Lipulekh, Kalapani, and Limpiyadhura would fall under. Therefore, the only question here would be the origin of the river. There have been records of the village chiefs of those areas sending letters to Prime Minister Chandra Shumsher about domestic troubles, and those address the Nepalese Premier as the head of government for their country.

Here's the source for the original text for the Sugauli Treaty : http://nepaldevelopment.pbworks.com/w/page/34197552/Sughauli%20Treaty%20of%201815%3A%20Full%20Text Here's the source for the letters (They don't show the contents of the letters, though. I'll put them in once I find them.) : https://www.peoplesreview.com.np/2020/05/26/chandra-shumshers-letter-proves-kalapani-limpiyadhura-nepali-territory/