If you are working with raw files, you don't get any options.
A raw file will first open silently in the Camera Raw plugin, where Lightroom adjustments are applied.
Then a new file, rendered from the raw file opens in Photoshop. This file will have the raw file extension, which can be confusing. It is just a generic RGB file, with no particular file type. When you save it, it will save as a tiff or psd (depending on what you have chosen under External editing in Lightroom's preferences), and return to Lightroom.
You only get the dialog with the options to save as a copy etc. with rendered files – i.e. jpg, tiff and PSD files.