I'm in Laos studying Lao on my own and came across the fact that different sources have slightly different words for "stairs" and the SEAlang Lao dictionary has even more:
- ກະໃດ - 15 Google results
- ກະໄດ - 7,400 Google results
- ຂັ້ນໃດ - 36 Google results, in an old Lao to English phrasebook found on my guesthouse bookshelf
- ຂັ້ນໄດ - 75 Google results, in current Lonely Planet Lao Phrasebook
- ຄັນໃດ - 8 Google results
- ບັນໄດ - 50 Google results
Except for the last one, they all seem like they could plausibly share an etymology as a borrowing from a language with different phonology.
For the second syllable / morpheme the two variants ໃດ dài and ໄດ dài have the same vowel quality, length, and tone. Lao shares with Thai the quirk of having two letters for the same /ai/ vowel sound.
For the first syllable / morpheme there are three possibilities, all beginning with a velar stop and with a short /a/ vowel: ກະ ká, ຂັ້ນ kʰȁn, ຄັນ kʰán.
But there are both voiced velars and unvoiced unaspirated velars and in the latter case both the high class and low class consonant letters may be used.
Also the syllable / morpheme may or may not end in a nasal. Either way it will be a "live" syllable as far as tone rules.
The resulting tones of both syllables end up having multiple possibilities as well.
กระได (kraˈday) and บันได (banˈday) seem to be the only possible Thai cognates. The second uses a first syllable / morpheme compatible with our last Lao word, which is not similar to the others so we didn't analyse further. But the first does seem sufficiently similar to all our other Lao words. Could they all be related? From whence do they originate?