This has been rattling around in the back of my mind for awhile, so I finally poked around a bit and came up with this chart from St. Paul Public Schools:

http://title1.spps.org/uploads/text_correlation_chart.pdf

It doesn't have complete conversion charts, but it does give you an idea of the range. Your private schooled child most likely does not have a Lexile because the school chose not to pay for the additional figure (it's extra). The Lexile is converted from the reading comprehension scaled score (SS on your report).

...pronounced like the long vowel and first letter of the alphabet...