Here is the definition of upper limit.
If I'm not mistaken, $\max_P$'s converse domain is the universal set $V$. The definition appears to be limiting the converse domain of $\operatorname{seq}_P$ to $\Lambda$. This is definitely not right, but what is wrong with my reasoning?
*Note: $\max_p$ is defined at 205.101.102
✳205.101. $\vdash:$$ x$ $ \max_P$ $\alpha$ $= x\in \alpha ∩ C‘P-P‘‘\alpha.≡ .x$ $\min(\overset{\smile}{P})$ $\alpha$
If I'm not mistaken, not all classes have maxima, e.g. (0,1) with respect to $\lt$. If $converseD‘\max_P$ means all the classes that have maxima, $-converseD‘\max_P$ means all the classes that do not have maxima. Based on the context, $lt_P‘\alpha$ is meaningless if $\alpha$ has a maximum with respect to $P$.