First, and most importantly, you simply need to ask them what atheism lacks that God has that grounds morality.
A perfect comprehension and understanding of the nature of the universe, with specific focus on his perfect comprehension of the nature of intelligence and that which is required for such intelligence to progress and achieve a "fullness of joy" which is the purpose of our existence.
That is, morality is the structural integrity of human relations: it is the attitudes, perceptions, and conduct within a relational context that creates the conditions for and boundary conditions of human happiness. God has a full and perfect comprehension of this ground, and hence, is qualified to identify it to us.
Second, you can bring up the Euthyphro dilemma. The gist of the argument is that if morality is contingent on God, it is arbitrary and empty, but if is contingent on something independent, then belief in God doesn't matter.
Why, if morality is contingent upon God (not that LDS doctrine claims this, but for the sake of the argument), need it be arbitrary and empty? Is this supposed to be a logical deduction? If so, we are missing a premise (premises) here. It would seem that for the contingency of morality to imply arbitrariness, this would require an assumption about the nature of God himself such that contingency and arbitrariness could be logically linked? What is that basis of that linkage?
If, for example, God is omniscient, then he has not only all true moral knowledge, but all knowledge of the manner in which morality should be applied to human affairs. If then, morality is contingent upon God, it is contingent upon a ground of absolute non-contingency (even if it is contingent solely upon him, his knowledge, being prefect, is non-contingent).
Far from making morality arbitrary and empty, contingency only points us to the source of moral knowledge, not its ultimate justification.
God only becomes unnecessary if independent contingency, or that upon which the contingency is based, is understood to somehow transcend God rather then exist as a, to borrow a term from physics, "field" in which God, and all created things, are embedded.
"morality" is an abstraction, and only achieves application as intelligent beings interact with one another. It is the nature of that interaction that is important. Morality then, is an emergent property in human relations, existing for human beings only as they are capable of interacting with each other in a moral way.
Morality, as with Priesthood law and the principles of the Gospel generally, coexist and are co-eternal with intelligence, and only intelligence can apply moral concepts in relationships with other intelligence. Hence, abstract principles and intelligence are interdependent and interconnected, making independent contingency simply an acknowledgment that God, while not the creator of morality, is he who identifies it to us and holds us accountable for our actions in relation to it and to him as the ultimate source of our own knowledge of the proper boundaries, channels, and limits of human relations.
God remains as necessary as before (as "lawgiver" and as exemplar (Jesus)) even though he need not be seen as the ultimate ground of the concepts themselves.
He is the ground in the sense that he is the authority that holds his children accountable for their actions in relation to eternal law (which he is capable of because he is an intelligence) but not the ground in the sense of the ultimate origin of those eternal laws
The alternative is, of course, morality that is contingent upon human notions of morality; that is, relative concepts contingent upon time, culture, social conditions, and various societal norms, mores, human psychological dynamics, passions, and emotional states.
One way to get the point across is to ask why you can't have what the theist has by grounding your moral views in the will of Gadianton? Why is that any worse?
Gadianton would have to have the attribute of omniscience, which he patently does not. Gadianton would also have to have God's character, which insures the proper moral boundaries of God's own dealings with human beings, which neither he, nor any of us, so have.