You will not be able to 'connect' IKEA remotes directly to other manufacturers' devices using TouchLink, due to the encryption key that only IKEA devices have (by the way, the same is true for other manufacturers supporting TouchLink - each manufacturer has its own 'secret' key

).
The remote should connect to the gateway using the classic connection (aka 'network steering' or 'classic join') (4 clicks of the pairing button) (but this Lidl one I see doesn't accept it).
Generally the gateway from LIDL is based on the TUYA ecosystem - and this has its communication layer on the standard ZCL Zigbee - presumably to avoid Zigbee certification/fees. Some of the devices work (e.g. light bulbs, which TUYA can handle on the standard Lightning cluster - but only to a limited extent - I don't think colors work from what I remember).