Some general thoughts... one approach I've used is to create a print file. You could send it off to either your printer or a print service. A rough overview goes something like this.
In LR, go the Print module. Prepare your print, size, dpi and max JPG quality. Check Print Sharpening, sRGB Profile, Intent, say, Perceptual and select
Print to File.
In LR, you also have an option for using a printer profile ( if you installed one in the profile directory) instead of sRGB that can be added to the file on saving. But I don't believe there is a way to soft proof in LR4. So you can just select sRGB for saving and then load the print profile in Photoshop where you can both soft proof and make final edits such as brightness and contrast.
Load the print file up in Photoshop and assign the printer profile (Edit->Assign Profile) and select the printer profile (if installed). Goto View->Proof Setup->Custom and pick options in the popup dialog for soft proofing. Now you can either save the finished results with the embedded printer profile or convert the image to the profile (Edit->Convert To Profile) and then save as sRGB stripping out the loaded printer profile.
You'd use the latter method of converting and removing the printer profile for services that do not read the embedded printer profile (eg Costco ). But for your own printer you can now print from Photoshop and configure your printer driver to read an embedded profile. There is still a bunch of detail I didn't cover and I hope I got right what I've written.