Okay. This gets a bit complicated. While no-one short of a search engineer can tell you what any search engine will do specifically, we know a few things based upon what Google tells us in a whole host of places. I will explain.
Google will parse the HTML DOM objects from top to bottom assigning each HTML element with an ID that will uniquely identify the HTML element, assign an order to the element, assign parent-child relationships between elements such as in ordered lists, and finally, when how one element relates to another such as paragraphs following a header. Using the IDs, the original HTML can be reconstructed as well as be referenced in semantic block elements and dependencies from one to another. Keep this in mind.
Also, keep in mind that Google will compare pages to know what HTML DOM elements exist on several or all pages so that it can properly identify content from other elements such as header, navigation, side-bar, footer, etc.
Semantics is based upon this.
Taking what we know, both of your list elements will be taken as templated HTML DOM elements separate from content. Your first list will be given more importance simply because it appears first, however, since you are using list elements (at least in your example), the importance difference would be small. Your example does not use the nav tag. I invite people to comment if this tag is necessary or important. I use it.
It may be to your advantage to use the tag to signal that both lists are navigation. The tag may help search engines see your navigation properly. Search engines, consider navigation as very important signals to your most important pages. Using the tag, in theory, should tie your two list elements semantically as important (navigation) DOM elements and weigh them higher than (templated) content elements.
While I am a believer that navigation should be as simplified as possible to avoid issues, I rather suspect that your two list elements should be seen okay. I prefer a single list element, however, I rather suspect having two lists should be fine. Just know that it is very possible that the second list element would be seen as less important, though not much. For this reason, be careful to keep this in mind and organize your links accordingly.