It seems that this issue is not caused by any behavior of LyX, since
merely adding LyX to a profile breaks the existing texlive installation:

========================================================================
~/tmp$ cat test.tex
\documentclass[a4paper]{article}
\usepackage{url}
\begin{document}
\end{document}
~/tmp$ guix environment --pure --ad-hoc texlive -- pdflatex test.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(./test.tex
LaTeX2e <2018-12-01>

(/gnu/store/wyp70a5a4spmj1g2wvm27d5968sssvwq-texlive-texmf-20190410/share/texmf
-dist/tex/latex/base/article.cls
Document Class: article 2018/09/03 v1.4i Standard LaTeX document class

(/gnu/store/wyp70a5a4spmj1g2wvm27d5968sssvwq-texlive-texmf-20190410/share/texmf
-dist/tex/latex/base/size10.clo))
(/gnu/store/wyp70a5a4spmj1g2wvm27d5968sssvwq-texlive-texmf-20190410/share/texmf
-dist/tex/latex/url/url.sty)
No file test.aux.
(./test.aux) )
No pages of output.
Transcript written on test.log.
~/tmp$ guix environment --pure --ad-hoc texlive lyx -- pdflatex test.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(./test.tex
LaTeX2e <2018-12-01>
(/gnu/store/xq0b0mgz5h6invz9fh13n29mb2jfdb0s-texlive-union-51265/share/texmf-dist/tex/latex/base/article.cls
Document Class: article 2018/09/03 v1.4i Standard LaTeX document class
(/gnu/store/xq0b0mgz5h6invz9fh13n29mb2jfdb0s-texlive-union-51265/share/texmf-dist/tex/latex/base/size10.clo))

! LaTeX Error: File `url.sty' not found.

Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)

Enter file name:
========================================================================

Regards,
Jakub Kądziołka