LVL Floor Joist Notch / Reinforcement Question
The engineered lumber should be marked with the name of its manufacturer. Each manufacturer publishes information about the size and positioning of cutouts that are allowed on a "prescriptive" basis. If you can't find a cutout or notch description in those tables then you'd need a structural engineer to design something specific for you.

The steel I beam approach you proposed may work, but it may not be necessary to go that far. It may be possible to simply reinforce the joist that is to be notched, for example by attaching a plywood or steel sheet gusset to the sides of the joist extending some distance beyond the notch.

An alternative is to cut out the marked part of the joist completely. A beam may be installed crosswise between the joists to the left and the right of the marked joist so that those two carry the load of the cut joist. Doing this is likely to require those two joists to be reinforced in some way, such as "sistering" them by installing a second joist alongside the existing joists. The "sister" might be dimensional lumber, another LVL of same or different depth, etc.

A structural engineer could help you figure the loads carried by the floor above and choose the "best" approach based on material cost, practicality of carrying materials into the space and installing them, etc.