The spell only permits the caster to vertically move the target. This makes it a great lockdown spell against a melee-only opponent as they can be lifted into the air and subsequently pincushioned, provided there isn't anything for them to grab onto.
The only form of lateral movement permitted by the spell is detailed in the spell's second paragraph which states that the target must push off of a fixed object within reach and when doing so the creature would use its climb speed to do so.
If the target were to elect to 'climb' as described in the second paragraph, they could potentially do so provided they remain within the 120' diameter sphere around the caster you described in your question. However, the caster cannot force them to move laterally and would need to rely on alternative methods to push the target around, perhaps a warlock ally with Repelling Blast.
The spell's restriction on range limits how high you can lift them up away from you: 60 feet. Usually close enough to target you with ranged weapons if they have them. It also determines when they escape from the spell if they climb away, since once they get outside of the 60' radius, the spell will end for them.