Q: “Courts are closed for the foreseeable future. Does that mean that there is nothing I can do on a pending lawsuit to which I am a party? Are there things I should be doing now if I think I might have a lawsuit to file when the courts do reopen?”

You are correct that courts, for the time being, are closed. What this means is that there are no in-person court appearances or hearings. While your lawyer can still work on your case (reviewing documents, preparing briefs, engaging in settlement discussions), as a practical matter, most litigation has come to a screeching stop. As such, your case will take even longer to resolve than it typically would, which is usually not quick, to begin with. Lawsuits can be filed electronically while the courts are closed. 

In terms of future litigation, it is understandable that most businesses do not want to pay lawyers now to litigate a dispute when there are more pressing financial priorities. This doesn't mean, however, that you should not prepare for future litigation either brought by you or that you think will be brought against you. You should continue to document disputes and issues by saving your emails or making contemporaneous notes. This will be very important to bringing or defending a claim later.  

One last point. There may be no better time to settle a lawsuit than when the world is in crisis. If you are a plaintiff pursuing damages, you may want to take what money you can recover now and move on rather than continuing to pay your lawyers. Adversity often brings opportunity.