Can we settle a dispute on our own?

Yes. There is no requirement that lawyers be involved in the settlement of disputes, even after a lawsuit has been filed. People and companies can resolve their differences informally. If they do, it is often helpful for such informal agreements to be reduced to writing. Where a lawsuit has been filed, if you agree to settle, the settlement agreements generally provide that the suit will be dismissed "with prejudice," which means that it cannot be re-filed. If the issues at stake are important, or a substantial amount of money is involved, it is a good idea to consult a lawyer, as inexperienced persons can inadvertently bargain away their rights.