The injured man Jessica Harris (posing as Dr. Smith) steals the jacket from is Bill Mumy, who played Will Robinson in the original series.
In the original series Penny found a pet alien monkey and named it Debby. In this series Don has a pet chicken and named it Debby
This series shares theme music from both the original series and the 1998 movie. The series theme is the most popular, however it was only used in the third season of the original series. The first two seasons of the original series had a different theme song. Both theme songs were composed by John Williams, who also composed the music for Star Wars.
Bill Mumy (the Will Robinson in the 1960's version of Lost in Space) became integrally involved in the 2018-2021 Netflix Lost in Space series not only making cameos appearances as Dr Zachary Smith but also advising the modern Will Robinson, Maxwell Jenkins. Max credits Bill Mumy's involvement in helping him greatly in his reprise of this critical role in the family.
The planet in season one of the new series borrows from an episode of the original series where the Robinsons were on a planet with a highly elliptical orbit that made that planet icy and hot.