Typically the term "Living Trust" is referring to a revocable trust because the trustee of the trust, (usually the grantor of the trust, the person who set it up and contributed the assets), is considered the owner of those assets. So if mom was the trustee until she passed the basis of the house to the beneficiaries would be stepped up to FMV at DoD. Any improvements made to the house from DoD to the sale would be added to that stepped up basis. The DoD value of the house would also be included in mom's estate for estate tax purposes.
However, Living Trusts can be created that are irrevocable. This is the case if an independent trustee was managing the trust while mom was alive. In this instance mom's original basis in the house would carry over to the beneficiaries.
Your wording - "mother had a living trust set up for her..." - suggests an attorney drew up the trust documents and that's the logical place to ask "was this a revocable or irrevocable living trust?"
