Adobe's website, under "Lightroom Supported File Formats", says it can open the type of images contained in this set. It is comprised of 22.4 Gigabytes of Data in this package (4 DVD's). 1,268 TIF Images. 411 PSD Images (Photoshop Files). 2 Brush Files (Umm - they look the same to me - so, really just 1 photoshop specific brush set - don't think this will work with Lightroom, but no worries. They were basic shapes only! Nothing fancy) 1 Tutorial PDF book. 2 Action Files specific to Photoshop. A bunch of Word Docs (*.rtf primarily, three .doc, 4 .txt files) outlining how to use their templates/actions/brushes and such geared towards use of Photoshop (Photo manipulation).
This is Clive. The creator of the 1500+ Digital Photo Backgrounds Package from which your question was asked. The short answer is no. Although the psd and tiff formats are fully compatible with Lightroom. The functions necessary to isolate, cut, copy and paste a subject to a digital backgrounds are not available in Lightroom. I use Lightroom and it is a great product, but it's primary function is to organize images with light editing in the form of color balance, spot removal, cropping, etc.
However, any version of Photoshop will work just fine. All the way from Elements to CS to CC. Without knowing your situation, my recommendation is to purchase a recent, but not necessarily latest version of Photoshop Elements and see if you enjoy the process. Elements versions of Photoshop can be had for about $40-$100.
BTW, tutorials are included as well as our free one-on-one email tech support. Also, we have a 100% Unconditional Satisfaction Guarantee on every product.
I hope that answered your question. If not, or if you have any other questions, feel free to contact us anytime.