Prologue Tree: Lambda-11

Bens Tree of the Proluge.

Branches

Lambda Branch

Ben will have a part where he discovers a Murakumo Unit that will activate and fight him. After the fight Ben will realize he is fighting Lambda-11. Upon speaking her name Lambda will be confused about how he knows her name and since She's operating more independently with Kokonoe Mercury too bust to be monitoring her closely, she will assume Ben is one of the missing Sector 7 Scientists (because lab coat) and ask for his assistance in her reconnaissance.
The split can either happen here, with Ben deciding to help her or not, or earlier, with Ben deciding to get into the fight or not. Maybe earlier since it seems out of character for Ben to turn down someone's request for aid.
This unlocks Lambda as a Fighter and unlocks her prologue tree.

The plot of this tree sees Lambda-11 Scouting Rollinsberg with Ben.

Encrountering Crona

The last Cell of this tress Trunk, invovles Lambda-11 and Ben Encuontering Crona/Ragnerok. Afraid and spurred on by Ragnarok, Crona will attempt to fight Lambda and Ben. Ben may not be available as a fighter for the in-game match as he outright refuses to fight Crona. After the match, Lambda will equate Crona to that slug she befriended (Tartar or Mr. Tartar) and decides to teleport them back to Sector 7 so they can be healed from the injuries after the fight. Lambda embraces Crona and they are bothe teleported, leaving Ben to be increasingly concerned about their disappearance.

Ben: Oh, they teleported. I'm sure it's fine, It's probably Kokonoe. ... Even though I haven't seen her yet and don't know if she's here. Hrmmmm... NOPE can't let it go. DON'T WORRY BABIES I WILL FIND YOU!!!
This unlocks more of the trunk in Proluge Tree: Ben