Lyx: can I export LaTeX without the preamble?

Not directly possible at the moment it seems, there is an open feature request for this in the LyX bug tracker:

• Ability to export separate preamble/content latex files for including in existing latex document

But there is at least one workaround described there:

Create a dummy master LyX file, and include the other file(s) as child documents. When exporting the master file, each child document is created as a separate .tex file, without preamble.