As a lucario & banjo co-main, I think the Zelda MU is even for both characters. For lucario, zelda is relatively easy to combo when we're at lower aura, and once we accumulate some decent aura starting at 70-80%, I find it's relatively easy to kill Zelda since she's light and we have very solid mobility to capitalize on the holes we find in her zoning with phantom (and her approach options are less than stellar if we get the stock lead). As long as we don't get careless throwing aura spheres for you to reflect back at us or mash on your shield and get sweetspot lightning kicked as a result, I don't see how this is a losing MU for lucario.
I admit upfront that I don't have extensive Zelda MU experience as Banjo, but I'll still explain what I've seen to be the case so far. He can definitely struggle to approach Zelda a bit more, since his all-around mobility is more limited than Lucario's, but I think it's doable for him to get in and do a number on Zelda with his strong ability to rack up damage quickly. Banjo is also considerably heavier than Lucario (106 compared to 92 units, respectively), which helps to compensate for his struggles approaching. We can mix things up with our 3 jumps (so we can wait out nayru's love if you decide to try using that as a get off me tool), use rear egg as a bait for you to use NL and give us a free wonderwing punish, and our 2-framing and ledge trapping abilities are also very strong. All this, plus Banjo's better neutral for playing keep away when/if he gets the lead, has me think this can't be anything worse than even.
I also secondary Shulk and am not sure how you think that match up is even given his range and ease of approaching with speed art and jump art (curious to hear your thoughts on this one though, as well as your reasoning for either Lucario and/or Banjo being winning for her). These are just my two cents on the Zelda MU with the characters I use.