I am so sorry for the loss of your mother.
You are not legally required to open up the estate.You have to decide if the lots here are worth the filing fees and a lawyer.In probate there is a priority of creditors and likely the estate would be insolvent if she owes a lot of bills.You may decide it is not worth it, eventually the cemetery plots may go back to the cemetery if there are dues or taxes due on them.
I would estimate probate here runs around $4-$5k with filing fees, again decide if is worth it or not.Legally you may decide it is not worth it , in which case you write creditors and them she was insolvent and no probate is anticipated and ask them to close out their files.
Often it is easier to just let the lots go here.A creditor can open probate, but that is unlikely since they aren't that valuable.I would consider letting them go here unless they have great value.Probate costs and the creditors will get it all here in all likelihood.
I do appreciate the chance to help you today.I wish you the best in moving on.
If you have not done so you are entitled to a one time payment from social security as her heir.Its a small amount $255 but it might help you with expenses.
Thanks again having gone through this recently I know it can all be overwhelming.