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Hi Anaid,
We have tested from our side. We can reproduce the same behavior in the secondary list as you described. We are afraid it's the expected behavior. Thanks for your understanding.
If you are willing, you may try to use Microsoft Power Automate flow to get data in the second list, not use lookup column. Then set view formatting for the secondary list.
To make sure you get the dedicated assistance about flow solution, we sincerely recommend you post the question in Microsoft Power Automate Community, it is the specific channel handling flow related queries, members and experts are professional and will assist you further.
Thanks for your understanding and patience so far.
Have a nice day and stay safe!
Best Regards,
Tina