Will we be able to see and speak with our Heavenly Father and Jesus in the Spirit World, or must we wait until after the Resurrection? Is it incorrect to say to someone if their loved one dies, “he/she is with the Lord now”?
To be with the Lord has different connotations. For instance, to be with someone could mean to agree with them. Two people could be assumed to be together in cyberspace when they are communicating by computer. Two people could be assumed to be together if they are in the same building, or the same room, or sitting at the same table. Yet, two people in each of those circumstances could not be together at all, being complete strangers one to an other. One thinks of being alone in a crowd.
When you speak of seeing and speaking with our Heavenly Father and Jesus, part of the question can be immediately answered by asking another question. Can you speak with your Heavenly Father and Jesus now? Of course you can, and I assume often do. Certainly that ability would not be eliminated in the spirit world.
But how about our powers of perception? We can speak with our Father without being in His immediate physical presence. In the spirit world will we be able to see an object without being in its immediate physical presence? I would be surprised if that were not the case. But the kernel of your question is will our Heavenly Father and the Savior visit the post-mortal spirit world, such that we would be in their physical presence. Well, the post-mortal spirit world for the spirits that inhabit this world is this very world. Here is a quote from Elder Ezra Taft Benson (later president of the Mormon Church) quoting President Brigham Young—
“The spirit world is not far away. Sometimes the veil between this life and the life beyond becomes very thin. Our loved ones who have passed on are not far from us. One great spiritual leader asked, But where is the spirit world? and then answered his own question. It is here. Do [spirits] go beyond the boundaries of this organized earth? No, they do not. They are brought forth upon this earth, for the express purpose of inhabiting it to all eternity. when the spirits leave their bodies they are in the presence of our Father and God; they are prepared then to see, hear and understand spiritual things. If the Lord would permit it, and it was His will that it should be done, you could see the spirits that have departed from this world, as plainly as you now see bodies with your natural eyes”. (Brigham Young, in Journal of Discourses, vol. 3, pp. 367-69.) (Elder Ezra Taft Benson, Life Is Eternal, Ensign (CR), June 1971, p.32)
That quotation would seem to answer your question. As spirits we will have abilities characteristic of spirits that are denied to the limitations of mortality, i.e. “to see, hear and understand spiritual things.” And the statement is made that we would be “in the presence of our Father and God.” That circumstance, however, I believe, would depend very much on the kind of lives we would have lived while in mortality. Speaking of the righteous in the post-mortal spirit world in D&C 138:18-21, we read—
While this vast multitude waited and conversed, rejoicing in the hour of their deliverance from the chains of death, the Son of God appeared, declaring liberty to the captives who had been faithful;
And there he preached to them the everlasting gospel, the doctrine of the resurrection and the redemption of mankind from the fall, and from individual sins on conditions of repentance.
But unto the wicked he did not go, and among the ungodly and the unrepentant who had defiled themselves while in the flesh, his voice was not raised;
Neither did the rebellious who rejected the testimonies and the warnings of the ancient prophets behold his presence, nor look upon his face.
So the answer to your question is: possibly, depending on who you are.