Mother received Medicaid recently and children are selling home. What is the lifetime value from the sale?

IRS has a Life Tenant & Remainder Owner interest table. Like 200k LT at 85 is .3535 / $70,718 with Remainder owner(s) are .6464 / $129,282. Personally I think you need a LL.M taxation atty to get it right. Not a DIY. A good elder law atty will have a LL.M they refer to.
Could be taxes & capital gains as well as Medicaid income issues. Nothing but FUN! & it really needs to be done correctly.

Steponme, the family needs to speak with an Elder Law Attorney because when it comes to "life estate use" of a house, your Mom still has "life estate use" even if she is now in a nursing home.

The Attorney will explain if the family can or can not sell the house at this point in time. Let the Attorney guide the family on what can be done, otherwise you may wind up with quite a quagmire.

You are talking about a life estate. There are actuarial tables that will calculate how much the life estate is worth and that asset amount will be part of your parent's assets for Medicaid purposes. You need to get either an attorney or the Medicaid case worker to tell you what percent her life estate is worth in terms of the home value. Life estate and proceeds from sale can disqualify Mother from Medicaid if you don't handle them properly. If you don't report them and it shows up when Medicaid is reviewed and renewed, it can cause a problem. The money from her life estate portion of the sale will need to be spent on your mother - better wheelchair, her share of meds, maybe clothes, etc. Get good advice, preferably legal on this.