As long as the lions act in consecutive
waves with each wave coming from a new generation, rather than a
simultaneous army from the same generation, then the lions can easily
win.
They merely need to attack in groups of
100, and wait for a full generation before the next attack.
The average lifespan of a lion is at
least 10 years in the wild. Splitting into these generational waves
of 100 lions will subject the sun to 500,000,000 attacks before it
burns out in 5 billion years.
And there will still be 950,000,000,000
lions remaining to rule the universe (although they'll be a bit
chilly unless they move on).