Hi everyone, I often read on here that DLs should be kept away from some plants that can steal water.
I have two DLs that are not really growing much, they are close to a juniper horizontalis (that one that stays "flat" and creeps). Is it a stealing water plant? Since I'm planning works I'm going to do to prepare the garden for next spring I could consider of removing it.
Many thanks in advance!

Those woody plants have roots that extend much father than the bush itself. I have pine trees that are 100' from my seedling beds and still every time I rework them I till up pine roots.

So I need to move it away from Dls!

Usually shrubs (they get large root systems) and trees are both bad for flower beds in terms of water and root interference. Plant things that are more shallow rooted, have comparable size root ball to the dl.
If you want something that is short and dark green spreading, you may try creeping phlox or even a sedum.

My queen palms forced me to build boxes. They would surround the lilies with their roots to steal fertilizer. The queens killed nearly half of the daylilies before I figured out what to do.

I moved the juniper, and to my surprise the roots were not spread all around. It was still a small juniper, so maybe it's because of that.
I also removed a delosperma cooperi (Trailing Iceplant or "Pink Carpet") and its roots were everywhere.
Now that spot has DLs only, I moved there three of them. I still have some work to do, but I feel better!

On this topic, then, is a Rose bush a bad neighbor for daylilies? How about boxwood?

rose bush on, boxwood-I think so, they get way bigger than the tag says usually, and they can have extensive root systems. Just be sure to water the dl more than the rose. roses don't usually need lots of water, well dl don't need it either-but do perform better if they get more water. roses must have well drained soil or they rot.