After verification and a lot of tests, the problem came not from Lyx but from the package used. According to the bibtopic help file, this package "doesn’t work with the ‘unsorted’ citation styles such as unsrt or unsrtdin.9 Use the package multibib.sty instead (see also section 8)."
So... Let's try multibib XD
BibTeX, biblatex and biber ⇒ Multiple Bibliography
NEW: TikZ book now 40% off at Amazon.com for a short time.
And: Currently, Packt sells ebooks for $4.99 each if you buy 5 of their over 1000 ebooks. If you choose only a single one, $9.99. How about combining 3 LaTeX books with Python, gnuplot, mathplotlib, Matlab, ChatGPT or other AI books? Epub and PDF. Bundle (3 books, add more for higher discount): https://packt.link/MDH5p