Much to my dismay...
In the modern parlance, the term 'lead pencil' refers to a mechanical pencil. As of 2019 this is a generally recognized fact, and most children, and indeed, most college students, will use this terminology exclusively. If you search for "lead pencil", the first result on Amazon or Google will be a mechanical pencil -- in fact, on Amazon the first 46 results are mechanical pencils, with the 47th being a set of traditional colored pencils.
The cause for this is simple enough; a pencil is just a pencil, but a mechanical pencil is different, and so requires a modifier... and 'mechanical' is too long for convenience. So what sets apart the mechanical pencil, other than the mechanics? The fact that one must reload it with lead. The next step in phrasological development was inevitable, if not entirely forgivable.
While there is no practical way to stop this corruption of common language, I will mention that Spanish, falling prey to this same linguistic rot (lápiz mecánico devolving into lápiz de grafos), obviated disaster by standardizing on the comparatively elegant portaminas, i.e., a "porta-graphite". Viva Español!