Is it ok if the Liing's carrier moves side to side when installed on the base?

Yes, there can be a bit of movement between the seat and the base. This is acceptable. Providing both base attachment bars are securely attached (you can tell this by lifting up on the carrier gently to confirm proper connection AND by visually checking that the release handle is not showing as red – BOTH steps are necessary), a bit of side-to-side play is safe and acceptable.