I would like to ask what is $\inf(\{30, 40\})$ and $\sup(\{2, 5\})$. I think that $\sup(\{2, 5\})$ is $20$ and $\inf(\{30, 40\})$ does not exist, but it may be $2$, but $5$ is on the same level and I don't know if I should consider the length of path to the node or not.
The diagram has a bottom element, in this case $1$ and a top element, $120$.
When this happens, every pair has a supremum if and only if every pair has a infimum.
The supremum of $2$ and $5$ does not exist because among their upper bounds there is not a least one, so there is not the infimum of $20$ and $30$, which are their minimal upper bounds.
Notice that if you delete one of the three lines: $2$-$20$, $2$-$30$, $5$-$20$, you obtain a lattice.