Lukaku was a great finisher for Everton last season, think he scored 24? But break that down and you will see he was scoring loads when Everton where already winning when there was no pressure on him, and mostly against weak teams.
Sterling has scored vital goals under intense pressure in dying moments of games with 10 or 11 men in the penalty box. That to me points to how strong mentally he is, otherwise he might have already gone the way of Renato Sanches given the amount of grief he gets.
But I agree with you he needs to keep improving to reach the very top and merit a place in first XI in a Pep team. Let's wait till end of season to get a full picture of his progress.
I'm not sure you can use the Bournemouth and Huddersfield goals as examples of this as one took a massive deflection and the other was smashed against him and looped over the keeper. He obviously did well to be in the right place at the right time, but they aren't examples of mental toughness.