I need to save an image from Illustrator at 150 LPI (lines per inch) for a printing vendor. How do I do this?
Bonus Question : Reccomended file format? (JPEG, TIFF, etc)
You can't control the line screen within Illustrator. That's an output device option and not a creation software option. For example, your home/office printer may have an LPI setting in the print dialog window, but that controls the output device, and does not change the artwork.
DPI = 1.5 x LPI
That means you need a minimum of 225ppi for most presswork. Standard is merely to think 300ppi since it's a round number. In addition 300ppi is acceptable for 175lpi as well. And 175 line screens are fairly common.
However, Illustrator, being a vector application, is resolution independent and doesn't have resolution settings for files. This is the nature of vector drawing.
Beyond those two items there are no other resolution options within Illustrator for reasons already explained.
As for format, the native .ai files is good, as is a PDF/x-1a file. In a pinch, depending upon the artwork, an .eps file may also work.
If you are concerned about some appearance aspects of the artwork, then exporting as a .tiff at 300ppi is also appropriate.
In almost no instance is jpg (or png) a correct format to use.
Actually, in terms of the file format, many service bureaus do in fact prefer JPG, depending on what workflow they are going to use. Otherwise, as a default, I would prepare a PDF, ensuring it is single layer and all fonts are embedded. The correct answer is: ask your vendor.