Lost Number has a high HP, 7000, and is a tough boss.
Save before the encounter
Make sure you save the game right before opening the safe so that you don’t have to repeat anything all over again in case you lose.
Attack using magic until he transforms
Lost Number transforms to either a physical or magical form when his HP halves. The last attack you make before the transform determines the form he will transform into. Since his magical form is much easier to beat only attack him with magic until he transforms.
Don’t use limits until he transforms
Don’t use the limit breaks that cause physical damage to lost number so that you don’t force him to morph into his more powerful physical form. See how to learn new limit skills fast. (See How to Catch a Chocobo in Final Fantasy VII (FF7))
Use physical attacks right after transformation
Right after the transformation use your physical attacks normally, in addition to the limit breaks you save.
Cast big guard on your party
If you have learned the enemy skill big guard then it might be very useful to cast it on your party. Make sure you cast it again when it runs out. (See How to win fort condor battles easily in Final Fantasy 7?)
Infect him with bio
Using Bio can be very handy in that battle as the commutative damage of poison can kill lost number or make killing him easier.
Attack with magic if he takes the physical form
If for any reason Lost Number takes the physical form then attack him with magic for he will be more resilient to physical attacks in his new form.
Stand in the rear row
If Lost Number turns to the physical form then stand in the rear row for his physical attacks are very powerful. This can help you survive while attacking him with magic.
How to defeat Lost Number – Shinra’s Mansion – FF7
How to easily beat lost number in Final Fantasy VII? What Level is recommended to fight the lost number?