Two Possibilities for Maakeh
Rav Moshe Taragin claims there are two shitot, regarding Maakeh, although they agree about Lo Tasim Damim:
Rashi(בבא קמא צא:) implies that both mitzvot apply generally, even to a mobile hazard, like a dangerous animal.
The Yam Shel Shlomo indicates that Maakeh applies to a fixed structure, while Lo Tasim Damim applies more generally, even to mobile hazards.
I have to admit, that looking at the gemara, I not certain that Rashi is even talking about Maakeh. The source seems pretty ambiguous to me, but it is certainly possible that I'm missing some detail that Rav Taragin doesn't mention explicitly.
Back to the Question of Connection
Regarding the Yam Shel Shlomo's opinion, our take on the Netziv seems to apply: namely that in the pasuk, Maakeh is stated as a specific mitzva, while Lo Tasim Damim sounds more general, and therefore they have different scopes.
Similarly, Rav Taragin's understanding of Rashi is like the Ramban, who thinks the scope of the mitzvot are connected. The only difference is that, while the Ramban contracted the scope of Lo Tasim Damim, Rashi expands the scope of Maakeh.