There is a very subtle difference between the two words.
The root خلد can be translated to English as "Ever lasting". It is used to describe objects that do not go away, and not necessarily people. The gardens of paradise are described as جنات خلد (Ever lasting gardens). Something like a memory can be described that was as well: ذكرى خالدة. Actual physical death might not come into the meaning. For instance, the name Khalid (such as from the famous companion Khalid ibn Al-Waleed) is derived from that root. It does not imply that the person is physically immortal, but that his other aspects (his reputation, piety, deeds ... etc) will be ever lasting.
On the other hand لا يموت is actually the combination of two words: the negative لا and the verb يموت (die). Here it is more concrete what we mean: immortality. Never dying.