A long storage life isn't the main problem.
According to the OP, it's going to be used regularly.
"... a 1 watt LED turned on for 30 minutes every 2 or 3 days for 80 years."
That's about 7300 watt-hours... a big battery, regardless of technology.
In theory, an RTG would do the job. More practically, over-specified NiFe cells and solar panels.
I don't think it's is worth spending any more time on this unless the OP gives a plausible scenario.