Don't ask me, I have no sodding idea!
As to your main question, I suggest you do some test pieces and, if necessary, increase the tip temperature by a few degrees and test repeatedly until you are getting consistently good results.
You might find that your new iron works with lead-free from the off. It's likely to have been made with lead-free in mind as the default since leaded solder is no longer used in new products.
I retired my dad's "antique" soldering iron recently. To replace it I bought a new iron. It worked perfectly. I don't know what temperature it operates at though, sorry.