Hello, new to the forums, hope I’m doing this right.
While Invasion is a terrific mode and Woody’s Lasso is a terrific skill, there’s no reason it should affect Invasion bosses. It’s designed to snipe squishy backline heroes, namely Maleficent, Megara, Elsa, Merida, Hiro, Merlin, Barbossa, Alice before she stomps you to dust, etc. It’s not designed to drag dangerous enemies like Mama Bots that spawn targets in front of it, into the middle of your team that has lots of squishy heroes like Zurg or Buzz.
If you run both Woody and Bo Peep in boss fights, Woody would pull the boss behind Bo and leave the team without tank in front. Then you also push the enemies further into your team should you use Bo’s active skill, since she starts facing left.
I would like to be able to run both Woody and Bo Peep in boss fights in Invasion, and not just because they are cute together 
Bo does great damage, and Woody is effectively the only semi-decent team healer for Blue. Where I’m at (O0-03, level 101 to 110ish), Felix is almost worse than useless. Genie is famously one of the worst heroes as well, and doesn’t self-heal (I was shocked he didn’t get a buff by the time live-action Aladdin premiered).
Blue Invasion is already the hardest one thanks to having terrible survivability aside from the likes of Hercules and using Megara, and not having any good team healing while Red & Yellow have tanks with all the tenacity and shields in the world, Mickey, Miguel, Sulley (Wo), Jack Skellington, Joy, Timon and Pumbaa now as well. Why make it even harder unnecessarily due to the boss in the middle of the team issue? (Which arises whenever you use heroes you are supposed to be using, namely one of the best tanks and one of the best supports in game.)
As far as I know, this problem is only relevant in Boss fights and shouldn’t be too hard to fix via a small change to Lasso (or making Mama Bots impervious to Lasso).