These are individual's school arrangement. I'm not sure about St. Clare's, but i know SH definitely allow students to join the lucky draw.
In general, private primary schools should allow its kindergarten students to join lucky draw, in which DSS primary schools do not allow to do so. However, some private primary schools might set ground rules against those who accept their offers to join the lucky draw. Different private primary schools have different treatments.
You may call and ask the schools. However, schools may change their arrangement year by year. Even now they told you they allow lucky draw, it doesn't mean 3 years later they still allow to do so. The schools are not binded to this arrangement.