Is the starter Aniimo viable late game?

Both starters carry a passive worth 30% more final damage when attacking without an elemental advantage. That means your starter does not need a favourable matchup to stay your main damage dealer. Against an enemy it has no edge on, the passive is what keeps its damage up, so you are not forced to swap it out every time the element chart turns against you.

Being viable as the main DPS does not mean it carries fights alone. Late-game and boss encounters call for a balanced team with healing and support, not a lineup of damage dealers. Keep the starter in the damage slot and spend your other picks on keeping it alive.

Does the starter you pick change this?

No. Lunara and Helion share the same elements, identical base stats in every category (ATK 116, 514 total), the same 30% final-damage bonus and the same combat role. Both are Light, also called Holy, so neither has an elemental weakness the other lacks. They differ only in play style and appearance.

Lunara is a ranged damage dealer, and her safer, longer-ranged pattern costs her no DPS against Helion. Her attacks that consume a Silver Moonmark stack also restore some HP, which helps her stay in longer fights. Whether she counts as a breaker or a healer on top of her damage is not settled, so do not plan your team as if she covers the healing slot. Pick on how you like to play, not on which one lasts longer.

Not settled: The Sun starter goes by more than one name (Helion, Caelion, Elion or Halcyon), and the starter lineup is sometimes given with Fenelon in it, so which Aniimo counts as a starter is not fully settled. The viability above applies to Lunara and her Sun counterpart.