You have two choices:
a) Grow the boot partition by booting from another OS (e.g. Ubuntu LiveUSB) and using "gparted" to shrink and relocate the storage partition by 256MB so the boot partition can be made larger. This is not hard to do, but normally a very slow operation even with an SSD in the box.
b) Make a backup of the current storage partition, move it off-box, then clean install the same LE version to get the larger (512MB) boot partition and then restore the backup you took.
I'd personally take a third option:
c) Make a backup oof the current storage partition, move it off-box, then clean install the latest LE version and then unpack the backup and selectively restore DB files and config .. then reinstall add-ons at latest versions. In short, do a spring clean of the install, but keep the essentials from the old.