Here are four different applications you can use to draw swimlane diagrams.
Each has its own benefits, so weigh what's right for you and your business and make a decision.
MS Visio - very powerful and tightly integrated with Microsoft's other productivity apps. It's not part of Office though and requires additional licenses which might be cost-prohibitive.
Google Drawings - Google's free drawing application which has many of the features of MS Visio and all of Google's pros/cons for their productivity apps.
Lucidchart - SaaS-based drawing application that has lots of useful features and functionality. It is paid, but they do have a free tier that allows you to see the software before committing to spending money.
MS PowerPoint - This shouldn't be your first choice, but MS PowerPoint does have the ability and functionality to draw swimlane diagrams. I mention it because many already pay for Office so this is an application you might already have.