Work With the Competition
If you have a nepotistic relationship with the competitor and recommend them then perhaps you can both be strengthened as category leaders.
Is the Lawsuit Cheap Marketing?
Anything involving Google and search is still a ripe field for media exposure. If you think your chances of winning are good enough, and the potential return is much larger than the risk of losing consider letting them sue you. It is probably not your fault that Google ranked you, but also seek legal advice outside of reading this post... I am not a lawyer.
Tank Your Rankings for that Keyword
If the links point at a page other than the homepage, consider removing the URL from your site, and then use the Google URL removal tool when the 404 error shows.
If you bought those links cash usually works to help remove them. Use their on site contact information and the email in their whois. Call the number in the whois data. Pay them to take down the links.
Improve the Rankings of Competing Pages
The tips offered in my search engine reputation management post work here as well. Follow the tips in that post to help make other competing pages rank better.
You can also work on improving the rankings of other competing pages while lowering your rankings. Feel free to push a couple strong pages if you are just trying to end the confrontation, but if you feel they are dirty you may also want to help surface some ugly news that was ranking on page 3. Do that and they may care less about your rankings, and shift their focus to those other sites.