What are the suggestions to run the 1.1KW motor using the 7.5kW drive? can we use it for lift application?

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It is allowed to use smaller rating motor with higher rating VFD for a temporary testing purpose by setting the motor control type to "V/F 2pt control", however it is not recommended to use for continuous operation. Hence you can not use 1.1 KW motor in 7.5KW ATV71 VFD for lift application for the following reason.

The minimum rating setting is possible only up to 0.25 In (In=VFD nominal current rating) in VFD parameter. It means VFD's motor current setting is limited to 0.25 times of VFD nominal current rating.
The nominal current rating of 7.5KW ATV71 drive is 17.6 Amps, hence the current setting is limited to 4.4 Amps (17.6 X 0.25 = 4.4) and the motor power rating is limited to 1.5KW in VFD parameter. If you connect 1.1KW motor it will not guarantee the protection to the motor and it is not recommended to use very smaller rating motor.