Photoshop (elements or full version) are 'image editing' programs. Lightroom is a 'workflow' program. The two are not necessarily interchangeable, although there is a significant amount of overlap in what they can do.
The best option, IMO, is to combine Lightroom with Photoshop (or elements etc.)
"filters" are pre-made effects that can be applied to images in Photoshop. Some of them replicate actual photographic filters...but many of them, are just the 'standard' effects that are built into Photoshop. I think they are lumped into the title of 'filters' because they don't have a better place for them.
When you see improved looking photos, it's may not be a 'filter' effect. There are many, many other ways to improve/edit/adjust images without filters.
You may also be thinking of 'actions' or 'presets'. In Photoshop, you can record a series of commands and then save it as an action...so you don't have to repeat steps over and over again. These can be exported and shared, so many of the common 'looks' you see on edited images, may have been made with the same 'action'.
In Lightroom, there are 'presets'. Basically the same thing...certain looks can be created, then saved and shared.
Some people are crazy for downloading actions & presets. And yes, they can be great time savers...but there isn't anything that they do, that you can't do yourself, if you understand the processes involved.
