Yes that’s not enough space.
I’m not going to talk you out of it. No space means no space. ext4 becomes critical at 90% and btrfs already at 80%. If the root directory is full, lightdm will not start because it has to write to the root directory. Write your data to an external data storage or another partition, not the root directory/partition, then there will be no problem.
What percentage is 3.8GB of the root partition?