LyX - multiline math environement left indentation

The term left-aligned in your formatting objective could be interpreted in several ways. Hopefully, one of the following two possibilities satisfies your objective.

The proper amount of kerning in the right-hand side solution will depend on the math font and the font size in use.

documentclass{article}
usepackage{mathtools}  % for 'matrix*' environment
begin{document}
[
begin{matrix*}[l]
  left{begin{matrix*}[l] abc \ def end{matrix*}right.\
  ghi\
  jkl
end{matrix*}
qquadtext{or}qquad
begin{matrix*}[l]
  left{begin{matrix*}[l] abc \ def end{matrix*}right.\
  % Kerning amount found by trial and error:
  mkern13.5mu ghi\ 
  mkern13.5mu jkl
end{matrix*}
]
end{document}