2.4W for 3 months, say:
3 months = 92 days = 2208 hours.
LEDs take 30 * 0.025A = 0.75A,
So battery capacity needed would be 2208 * 0.75 = 1656Ah, or 470 of those cells in parallel!
Normally if you want a lot of stored energy you'd go for 12V or 24V batteries anyway and buck-convert down to 3.3V or whatever.
Your energy requirement is over 19MJ, which for a 24V pack would need 220Ah, which is something you would actually be able to source, and it would be massive and expensive.
But your idea of fitting this in 40cm x 3cm x 15cm is hopelessly unworkable because batteries don't have that sort of energy density. Lithium chemisty goes up to about 250Wh/kg and you want over 5000Wh.