Are some soldering iron tips unsuitable for lead-free solder?
Lead-free solder requires higher heat. Lead has a lower melting point which one of the reason it was used in the first place.

You can find more information here:

http://en.wikipedia.org/wiki/Solder

which discusses both lead and lead-free solder.

I hate lead-free solder and do not use it when I am not forced. 

Edit:

http://en.wikipedia.org/wiki/Soldering_iron#Tips