'Low Saturday' is Easter Saturday (i.e. the Saturday of Easter week, which starts on Easter Sunday - tomorrow). So Low Saturday is Saturday 27th April this year.
www.catholicculture.org/culture/liturgicalyear/calendar/day.cfm?date=2019-04-27
In my RC parish, last year's palms are collected in the weeks coming up to the start of Lent. They are burned outside the church in a prayer ceremony on the eve of Ash Wednesday. The resulting ashes are used to mark foreheads of worshipers at Mass on Ash Wednesday, which is the start of Lent.
Right before the Easter Vigil Mass (tonight) a Paschal Fire is lit outside the church and the celebrants, choir, altar servers and congregation file into the darkened church with each person bearing a little candle lit from the Paschal Candle, which the celebrant lights from the fire. The symbolism is Christ the Light of the World, light/darkness, Resurrection/death.
Sometimes this service of light can be done with a small, sheltered fire and the congregation inside the darkened church, with the light passes to everyone's candle along the pews. We have had snow/sleet/hail/driving rain here at Easter - weather plays a part in determining the way the service of light is carried out.
This is not the night for burning palms. There are two fires associated with Lent and Easter, which are distinct.
www.catholicculture.org/culture/liturgicalyear/activities/view.cfm?id=1043