Under WA child custody laws can I get sole legal custody of my child if the biological father is in prison

Being in prison for life likely rules the father out as a candidate for custody of the child since the child cannot live with the father in prison.

(You likely should review with the appropriate persons whether your child should have continuing contact with a person in prison. Depending on the facts, continuing contact may be appropriate for your child.)

The fact that the father is in prison does not mean that you will have custody of the child. If being with you is not in the best interest of the child, the court can order that the child be placed with some third party.

You likely should review your facts and options with an attorney who can advise you how to obtain the parenting plan and other orders needed in your case.

Because father is unable to be the primary residential custodian of the child, you would (assuming you are not found to be unfit) be the primary custodian. However, depending on the age of your child and the relationship with the father, the court may order some sort of contact, such as visits or correspondence. Depending on the circumstances, you may be able to terminate the father's parental rights. I do not handle terminations, so am not sure if you need someone else standing by to take over those rights (such as an adoption), but you may want to contact an attorney that handles terminations to check on those options.