This is incorrect.

Elements is fully capable of handling a RAW file and does so with the same Adobe Camera Raw converter that Lightroom and Photoshop use. When you're working on a RAW file in Elements it's in 16-bit mode.

The only difference is that Elements cannot SAVE a converted file in 16-bit mode (such as a TIFF). For most peoples' uses, this doesn't matter. They don't really need a TIFF (or other file type that supports 16-bit). The 8-bit JPEG that Elements is able to create is fine for printing or online display or sharing via email, etc. etc. In fact, many printing services prefer an 8-bit JPEG... some even refuse to work with TIFFs or anything else. An sRGB color space is also what's normally used (recommended for online display).

A pro might need TIFF for a customer and/or CMYK color space for commercial printing purposes (i.e., printing presses of various types). But many of them still work with 8-bit JPEGs a lot of the time, to saves space and makes for faster image transfers. And, at times it might be desirable to save a file in 16-bit form, to come back to and do additional editing later.

Many inkjet printers can handle 16-bit files... but the only difference is that the print job will run slower than an 8-bit file. The end result won't be any better.

Your eye can't distinguish the difference in a finished image. 8-bit is already more colors than you can distinguish visually.

16-bit is important while doing image edits and adjustments. And Elements can and does do that, same as Lightroom and Photoshop. As with them, you simply work with your camera's RAW files (note: most DSLRs shoot 14-bit or 12-bit, but the files are interpolated as 16-bit by the software). The reason is a much greater range of colors to work from. 8-bit's 16.8 million colors seems an awful lot, until you consider that the 16-bit palette has 237 trillion discrete colors to work with.

So, for most people the "8-bit limitation" of Elements is actually a non-issue.

In a lot of ways, Elements is also more of a stand-alone, complete organizer and editor than Lightroom. For example, Lightroom cannot work in layers, such as might be used for selective edits. Photoshop and Elements can.... it's sort of a light version of Lightroom and Photoshop combined. Elements and Photoshop both have much more precise clone and healing tools than Lightroom, too. If you want to remove a complex object or combine multiple images in any way, it's impossible in LR. You'll need Elements or PS. There are other things that the editing programs can do, that Lightroom can't.

Lightroom is a powerful organizer and archive management tool... with minimal, quick image editing features. Photoshop is a powerful image editor... with little or no organizing and management capabilities. The two are designed to complement each other and - although some people manage with just one or the other - most people who use them need both. Photoshop is now only offered via subscription. Adobe no longer supports CS6, the last version of Photoshop that was available with a perpetual license. This means it won't be updated with new features found in PS CC and that it cannot support RAW files from newer cameras. That's no problem if you don't need the new features and use an up-to-date version of Lightroom 6 to convert the RAW, prior to passing it off to PS CS6. But if you don't already have PS CS6 (or an earlier version of PS CSx) that is adequate for your purpose), you pretty much have to subscribe to the package that includes both LR CC and PS CC.

Or, just buy Elements 15, if you don't need or want the extensive capabilities and the steep learning curve oof the LR and CC combo. Elements also has built-in learning modes for beginners. It offers three user-selectable interfaces: Beginner, Intermediate and Expert. You can start with one and advance to the other or switch back and forth any time you wish. Neither LR nor PS has any sort of built in support... so figure on taking classes or a series of online tutorials and buying a bunch of books to learn to use them well. There are "how to" books for Elements too, that might help initially, although you may be able to just jump in and start using it in one of its more supported modes.

There are many online comparisons of Lightroom versus Elements versus Photoshop.... Beware though, that they are talking about current versions. For example, https://photographylife.com/lightroom-vs-photoshop-elements/ is discussing Elements 11... and a heck of a lot has been added since that version (Adobe has a side-by-side comparison of version features on their website). Elements 15 is far cry from versions five or more years ago.

Photoshop is now available by CC subscription only.

Lightroom is available either by CC subscription or as a perpetually licensed version ($142).

Elements is only available as a perpetually licensed version ($80.... currently there's an offer that included Premiere for videos at no additional cost).

Any of them can be downloaded free from the Adobe website, for a 30-day trial. That might be enough time to test drive Elements or Lightroom (one at a time, I'd suggest)... but isn't anywhere near enough time to get started with Photoshop. I'd only suggest the Photoshop 30-day trial for fairly experienced users of earlier versions of PS.