Lightroom to Edit in Photoshop file type is JPG and not TIFF or PSD as selected

Sounds like perhaps the original file is JPEG, and when you send it to Photoshop you choose 'Edit Original' in the dialog below. If you tell Photoshop to edit the original and the original is a JPEG, then that is what you'll get in Phtoshop: that JPEG.

to put some flesh onto GoldingD's apt and concise question:

There are two workflows by which LrC passes images into Photoshop: 1) pre-saved file, and 2) unsaved image.

• When you are coming back to re-edit an image that was previously sent out to PS for editing. PS opens the pre-saved file conventionally, and that is what it reports as its document window title.
• In the case of version incompatibility between PS and ACR / LrC, also when a named external editing preset has been used, also if the external editor is a non-Adobe one: the same thing happens - not only for re-edits, but also for the initial edit. It will have been LrC that renders Raw conversion settings (if needed), and the current parametric adjustments, into pixels and then saved the result to disk. Again, this actual filename is reported as the document window title.
• Only in the case of compatible ACR / LrC versions, and only for an initial external edit not a re-edit, LrC sends PS the location of the source file and also the needed parametric Raw conversion / image adjustment metadata. PS calls in ACR to render everything into pixels held in memory, and then passes that into the PS editing environment as an entirely fresh, not yet saved image.

This image (in memory) has no actual filename as yet. It might as well be named "Untitled-1".

But to be more helpful, PS instead identifies it by the original source file on which it has been based. Thus it may show a camera Raw filetype - something which PS could never have opened directly. Or JPG. This does not mean you are actually editing a Raw or a JPG. You are merely editing something which has been derived from such a file. 

When you then Save within PS, the situation solidifies. An actual working file is created on disk, of the chosen type and suitable to hold layers etc - almost always PSD or TIF - and that hereafter is reported as the PS document title. Also, that is what gets imported to the LrC Catalog.

Are the images you are working on in LrC RAW or JPEG?