Okay. I think I figured out LR2's Rival system and I'll will post a guide on how to use it. Hopefully this thread will be used to exchange LR2IR homepages so we can all rival eachother and such. Anyway, here goes.
Rival Guide
Step 1: Make a Lunatic Rave 2 Account. ( this is done when you first open LR2)
Step 2:: Make sure your LR2 is set up for online mode:

Once you have made sure your settings is for Online mode, go into LR2 game like normal, the black screen will tell you your ID#.
Also you might want to play 1 song complete, regardless if its fail or clear.
Exit LR2.
Re-open LR2 window, and then go to the IR page from that select button Highlighted
Step 3: Head to your IR page (internet ranking page) via the selected button seen on the screen shot above.
1: Account name. This is the account name you chose for your IR account. It is changeable
2: Account ID. This is the Account ID you have, this is how people know who you are. This cannot be changed
3: Log out. -self explanitory-
4: DO NOT CLICK THIS LINK. Well, you can. If you want to delete your account. If you click that link you can choose whether or not to confirm the deletion.
5: My page. This link returns you to your homepage for IR.
6: Insane BMS charts, which are a whole new scale that goes to 24 (on singles) where AA [A] is equivalent to a 1, Scorpion Fire I think is a 5, and Mei's something like an 8.
7: The list of all songs sorted by how many played each song in descending order.
8: The list of the LR2 class courses. Click コースリスト(☆1-☆10)のダウンロード you should get a course.lr2crs file (the one with the filled star has the Insane BMS class courses, and doubles is at the bottom).
Place the file anywhere, and then open LR2 and drag the file onto the config window. It should say a message about 10 courses, and if you accept it will add them and delete the course.lr2crs file automatically. It will add courses that include songs you don't have, but it won't let you play those courses.
9: is advanced search. Songs are automatically added if they are played by anyone while they are connected to the internet ranking.
10: LR2IR history.
11: Search bar
Step 4: Searching for a rival. On the search bar, make sure the button that is 3 spaces from the left is selected. Put the user's name you wish to
search for and press enter.
A list of names should appear( if not just one) click it to go to that rival's IR page.
Step 5: Attaining the rival. When you find your rival's page you'll see his details and all the other good stuff

The button on the left takes you to the ghost battle record. You can see how many battles you won, and the stats for each song.
The button the right is registering the rival. When you click that button, you will return to your IR home page. Click"

"to save your settings and voila. You just earned youself a new rival.
Step 6: Once you have you rival a folder ingame should appear with your rival's name.

Inside the folder there are all the songs you have, that your Rival also has.

If you follow the guide, and get results similar to that, you have successfully registered a rival in LR2.
Enjoy.