Whether it be in a cover letter or on an interview (probably both), you will need to explain to a potential employer about your past lateral employment moves.
With respect to theme, think about it as your “career objective.” In an ideal world, your career objective is consistent and specific, making all of your past moves deliberate, planned, and necessary. In other words, all of your lateral moves make sense. You are not someone with “happy feet,” a job hopper, or always thinks the “grass is greener.”
These are all good reasons for having moved and should hopefully fit into your narrative:
Geography: You lateraled to another firm because you needed to relocate. Perhaps your significant other obtained a position in a different city, you are moving closer to family or friends, or returning to a place you once called home.
Moving with a Group: If the partner you primarily work for laterals to another firm and invites you along, this is not truly considered a lateral move. It’s a great sign that your partner values you so much as to bring you along to the new firm. This, in fact, should be included on your resume.