The restriction to see only 200 pictures in your photostream is indeed a pro-only feature that you can properly work around only with some dough.
If you download 200, then delete them, do a new 200 become visible?
From an answer to another question, this isn't impossible:
[…] Flickr will also only list the last 200 of your photos. Your older photos are there, flickr just doesn't list them in your photostream. If you have the urls you can still access them.
However, the pictures you are able to download from a free account (even if the free account was your own) are downsized (and compressed) versions! So, unfortunately, the only way to access your originals is to upgrade to Pro. They are still at Flickr's servers in case you'll upgrade, but they're just not accessible.
And as a last note, some Flickr → Lightroom tools can be found from a previous question: How to import photos and metadata from Flickr to Lightroom?