Is this Program able to change the Background of PDF files

If you want to retain the vector and layered nature of the contents of this PDF, you could bring that into a vector editor such as Affinity Designer, or Adobe Illustrator, or similar. Then the text and the background will be separately controllable and the text remains proper text - which will print crisply and even remain editable. Adobe allows a short one-off trial of Illustrator, which should last long enough to carry out the task. To continue using Illustrator after that trial ends you would need either a single-product subscription plan, or a subscription plan for the all-apps bundle which includes that (much more expensive).

Affinity software is IMO more consumer-level in its pricing, and its perpetual license rather than subscription. It may not be quite as maturely developed, or as industry-standard as the Adobe software is - but no complaints about its feature set. Personally I would be considering buying that in your situation, especially if similar tasks may occur again.

If you bring a PDF into Photoshop it is likely to just get turned into a bitmap graphic all on a single layer at the requested PPI resolution. You can still lighten that whole thing strategically, possibly in a way that maintains the blackness of the text (assuming it is black text) - but will have dumbed it down graphically. Not recommended.

Lightroom is not able to do anything with a PDF.  

Lightroom Classic has the capability to create a PDF slideshow and in that process do a little customization of the background during the creation process. However, there is no provision to modify an already existing PDF file.