Main reasons for using the Lance on Shingen:

With the additional 15 BG she gets from her first skill, you can ensure that she can burst after using Provisional Forest. With Michael you can directly Burst on the same turn if Shingen has 95 BG.
Additionally, you also wanna ensure that she has enough BG when you reach your next PF-Cycle, which you pretty much do with the extra BG aswell. Outside of that, she can also happen to have a single Burst during your PF-Cooldown, which speeds up the BG of your Hime aswell.

In conclusion: Lance gives you just so much more safety when it comes to BG gain and buffed FBs.