Wondering =notching out floor joists
Notching a load bearing joist is often big trouble, although unfortunately it is very commonly done by HVAC and plumbing people to accommodate their needs. Strapping a joist refers to installing a metal strap on the tension side of the joist, and can be effective. I assume you mean lag bolt (not blot). I am not sure why you include lag bolting with strapping, usually you do not lag bolt the straps.
Lag bolting is a technique to allow you to sister a joist, however if the first joist needs to be notched, probably the sister would also need to be notched, so you may not regain enough strength that way.
A tub can be very heavy, a cast iron tub can be >300 lbs dry, and if it holds 50 gallons that would be almost 400 lbs more if full, and this load is only distributed over two joists at best. If the tub happens to be near the center of the span, this is a large point load on the joists, and is best evaluated by an engineer or architect. Its a tough day when your tub full of water and a bather falls through to the lower floor.