So I think if you're the Cubs the questions you have to ask yourself from here as you fill out the roster are:
1. Do both you and Tucker feel comfortable having him play CF and/or 1B?
2. Of the non-Shaw kids at Iowa, which one(s) are you comfortable giving MLB at bats to in April/May if there's an injury?
Adding a 3B to the bench is a given. But the answer to these two questions colors whether you also add a CF, a 1B, or both. Plus how to weight the allocation of resources between those bench spots.
3. Is Luzardo the SP you wanted, or is he the SP you basically had to pursue if you couldn't find a satisfactory Bellinger deal?
With ~$40M to play with, adding a $15M SP like Dylan Cease is pretty doable. Hell if you gave him an extra year to keep the AAV down adding a Jack Flaherty wouldn't be insane. So now that you do have options it's probably good to confirm you're pursuing Luzardo because you think he's a GUY not because he's the best guy you could get for a sub $10M salary without blowing up the farm.