if you are reduced to 0 or fewer hit points by an effect that otherwise leaves your body intact,
(Trigger for the knight’s loyal beyond death, Player’s Handbook II pg. 27)
Every time a single attack, spell, or effect would drop you below –10 hit points or otherwise kill you,
(Trigger for the death delver’s nine lives, Heroes of Horror pg. 94)
If your hp goes down to somewhere between −1 and −9, loyal beyond death triggers and then, with that active, dropping to −10 or below would not “otherwise kill you,” and so shouldn’t trigger nine lives. Loyal beyond death expiring, however, would be an “effect” that would “otherwise kill you,” so it would trigger then.
Nit Picking—Possible problems, but should be ignored
There’s a bit of a nit here that nine lives says “drop you below −10 or otherwise kill you.” Without that “otherwise,” nine lives would trigger at −10 even if loyal beyond death means this wouldn’t kill you. With the “otherwise,” we have a problem: the English grammar itself assumes that −10 hp means death, which isn’t true in this case. We have to ignore part of this clause—but you could argue the part to ignore should be “otherwise,” in which case nine lives triggers. But the more reasonable reading is to see “drop you below −10 hit points” as kinda-sorta “reminder text,” and it’s the killing you that’s actually important—so if dropping to −10 hp doesn’t kill you, we should ignore that instead. That would mean nine lives doesn’t trigger until loyal beyond death runs out.
The other issue is, if you drop from 0 or higher directly to −10 or lower, you trigger loyal beyond death and nine lives at the same time, rather than triggering loyal beyond death distinctly before nine lives would otherwise trigger. Simultaneous triggers are not defined under the rules—the FAQ suggests that the general rule of thumb should be to apply them in the order most beneficial to the creature who controls them, and wide community consensus almost-always does exactly that, but that isn’t an actual rule. In this case, applying loyal beyond death first just makes sense, though—its trigger is, in a sense, “earlier” since it starts at −1 instead of −10, and it would be very weird for this interaction to work if dropped between −1 and −9 but not if dropped straight to −10 or lower.
Technically, these issues are enough that the “true” answer is that this is up to the DM. But a ruling against this combination is a red flag in my mind, that the DM hates you, personally. This is an incredibly weak 30th-level character; actual invincibility is old hat by that level, and this character has little else going for it.