How to claim a deceased's settlement from a lawsuit?

In this state, you would need to be appointed personal representative and be issued formal papers called "Letters of Administration" before you can defend or file any claim.  As an adult child, you have priority to ask for this position.

Note that you would need  personal representative authority to handle the claim (the attorney handling the lawsuit should not discuss settlement until you have this authority) , then must pay any probate taxes and disburse the money in accordance with the intestate laws.

If you have not yet opened an estate, you may want to contact an attorney in this state to help guide you through the process.   I hope that this answer helps point you in the right direction.

You should contact the opposing party in the lawsuit and assert a claim on behalf of your father's estate. 

When there is no will, intestate succession rules apply to determine the share  potential beneficiaries receive.  If your father does not have a surviving spouse, then the estate goes to the children.  If there is more than one child, each receives a proportionate share.  For example, two surviving children, each receives one half; if there are three children, each receives one third, etc.  If you are the only child, you would receive the entire estate.  If you are the only surviving child, your siblings children would receive their share(s).