Oh! Okay, sorry! Now I understand your question:
“Who do some Lao people use Lanna scripts in Buddhist scriptures?”
Lanna script, also known as the “Tham” alphabet/script (Lao Tham = Old Lao) derived from the Pali word “Dhamma”. The Tham alphabet were used particularly for religious and academic writing text in the Pali language on Buddhist palm leaves, manuscripts and books in Laos.
Why? Because the Tham alphabet was better suited for pronouncing the Pali consonants & vowels than the Lao alphabet.
Traditionally, only secular literature was written with the now standard Lao alphabet that was slowly standardized in the 14th century during the Lanxang Kingdom.
And because Theravada Buddhism came from the ancient Pali & Sanskrit people from India, the Tham alphabet was best used and suited to fully retain the original Pali Buddhist sutras and chanting, without changing the pronunciation or losing the full meaning. Very much like the Quran, it has been unchanged for thousands of years, and is refused to be translated into other languages, because it can change the meaning of the religious text.
Not only was it just used for Buddhist writing, but the Tham writing were used for scholarly records, like medicinal usages, poetry, scientific researches and how to make love potions in Laos.
And an added bonus of info: The Lan Xang kingdom (Ancestor of Laos-) held a special and close relationship with the kingdom of Lanna from the 13th century until the 18th century. The kingdoms were trading partners (as the two states came into a union against the threat of the Burmese and Siamese, as Lan Xang as the protector-) and not only actively traded fabrics, spices, etc. but also Buddhist folklore stories and poetry preserved in palm manuscripts.
Even after the Burmese invaded Lanna kingdom and the ties between Lanna and Lan Xang was cut, Lanna refugees (mainly nobles and even literature masters-) fled to Lan Xang (notably Luang Prabang), where they continue their cultural exchange.
That is why the Lanna and Lao language is nearly identical in ways and why sometimes (as seen in the example above-) “borrow” each other’s languages / dialect.
I would recommend you “Paths of Conflagration: 50 years of Diplomacy & Warfare in Laos, Thailand, & Vietnam" by Mayoury and Pheuiphahn Ngaosyvathn if you want to find out more. c: (Yaaay, Lao historians!)