On the LyX menus, go to
Insert | List/TOC | BibTeX Bibliography
This will insert a "BibTeX Generated Bibliography".
You now need a *.bib file as a BibTeX database. If Evernote exports a proper BibTeX database as a *.txt file, you just need to rename it.
Selecting the context menu ("right clicking") over the "BibTeX Generated Bibliography" will open a dialogue box that will allow you to navigate to and select your *.bib BibTeX file.
Then, on the LyX menus again, you can just use
Insert | Citation
to cite any of the references from your BibTeX bibliography in your document.
Note the BibTeX "databases" (or files really) are quite easy to write and edit by hand.
Emacs has BibTeX mode
if you need some clean up and additions to the Evernote export.