How can I dispute a lawsuit from my former landlord and possibly counter-sue due to a bed bug infestation in my building?

You can file a counterclaim if you have been sued. But you have a limited time to do so. You may have a valid defense to the claim. But you should act fact, as most deadlines for filing pleadings are strict and you do not want to miss out.

Whether you have any viable claims against your ex-landlord is highly dependent upon the exact details and facts such as whether you were responsible for the bedbugs to begin with and, even if you were not, did you give notice to the landlord of the problem and allow legally adequate time for them to fix the problem before breaking your lease? These and many more questions can only be answered by reviewing everything in detail with a local landlord-tenant attorney - and you need to do that immediately if a lawsuit has been filed against you since there are time deadlines already running against you. See a local attorney now - it could save you a lot of money in the end!