But as for the people, not really sure what to say. So I'm going to look at the Gospel Principles manual, the chapter on this topic, and see if it gives my mind more ideas. And today I will probably add quotes from the manual.
"The people who covenant with the Lord and with whom the Lord makes covenants are known as the Lord’s covenant people. Members of the Church are part of the Lord’s covenant people."
The manual points out that we make more than one kind of covenant. Baptism is a covenant. So is the sacrament. All of the temple ordinances are us making covenants with Heavenly Father.
The manual continues to mention that the Lord has made particular covenants with groups of people. I think that's where my confusion of what to say comes from. I hear the phrase "Lord's covenant people" and I immediately think about a group of people, like the Israelites. The manual refers to the Abrahamic covenant:
Then there is, of course, the members of the Church. Considering the covenants I mentioned before, that would definitely make LDS Church members a covenant-keeping people.
So what I'm learning is that the Lord's covenant people means, basically, anyone who covenants with the Lord. But I think more importantly, it is anyone who is diligently trying to keep those covenants.