Can the Xiaomi Induction Cooker Lite be used on top of a gas stove stand?

No.
Note 1: 
Do not place this product in an unbalanced, damp, or close to other sources of fire or heat (ensure a distance of ≥30cm between this product and sources of fire or heat).
Note 2: 
Do not place the product near devices susceptible to electromagnetic interference.
Note 3: 
Avoid using non-professional cookware to prevent affecting heating performance or causing hazards. If using other cookware, please adhere to the following: the cookware must contain iron, have a flat bottom, a diameter not less than 12cm, and not exceed the heating area.
Note 4: 
Before heating the cookware, ensure there is 'food' inside the pot to avoid dry heating. Exercise caution with cookware with metal handles to prevent burns.