All the sixes in the tarot deck, including the Devil and the sixes of each suit, relate back to the Lovers. Six is the number of Service and Healing, so all these cards have something to say about your behavior and interactions with other people, either with a particular individual, a group, or society in general. The emphasis here is on the responsibility (ability to respond) you take on when you engage in healing work and/or service to the greater good.
The lovers reminds us that the commitment in a healthy relationship must be to the quality of that relationship, not necessarily to the other person or people involved. If the Lovers card comes up in your reading, it means that you tend to do just about everything in your life with a full focus and energy investment. Your relationships tend not to be at the level of 50/50 but closer to 100/100. You have made a commitment to provide the support and permission, to hold the space that supports the highest good for the party or parties involved, to allow the best and highest potential(s) to manifest. This is the definition of a healer. one who provides the support and permission that allows someone to heal himself/herself if that is what (s)he chooses.