Besides the fact that Lukaku has proved to be a very unstable player... we must remember that he arrived at Chelsea as one of the great strikers in world football. After shining with the Milan shirt, Chelsea paid 113 million euros for him, however he ended up being a disappointment, would Liverpool be different? It is risky to make this prediction.
I think a more certain destination for Lukaku would be to return to Milan.
Lukaku is a good player but it seems he does not play well in Premier League. In Serie A, at least in Inter Milan, he can play better than in Premier League with Manchester United and Chelsea. However, we also know that in Premier League, Lukaku revived his career in West Brom
I still have feeling that it is not about Premier League but about the tactic of a team he is playing in. So in rest of his career (he is no longer young), he must be careful to choose a club to play for. It can be a club in Premier League or Serie A but tactic is what Lukaku must look at as his first priority.