A lighthouse allows for a safe return to the island it's built on without the boat being destroyed.
If there is a lighthouse on an island traveling there will never make the boat crash. And the opposite is equally true: if there is no lighthouse on an island traveling to that island will always make the boat crash. To verify the existence or not of the lighthouse on an isle, the player can check the map.
Exception: if the Monarch loses the Crown, the boat will break, even if there is a lighthouse on the first island—that is where heirs start their journey.
In order to build a lighthouse, the Monarch must first send troops to destroy the dock portal. When the quay is cleared, the Monarch can pay six coins while at the very end of the dock to build a wooden lighthouse.
The structure is built instantly, without the need of builders.
“ The lighthouse can only survive a certain amount of days.—Gordon  „
When Monarchs leave an island, the lighthouse built on that island is susceptible to decay. But it will only start decaying, if the island where it's built on has no (or no more) walls. Either because no walls were built when the Monarch was on the island, or because the walls built there have all decayed after the Monarch's departure. This is when the preset lifespan timer of the lighthouse (mentioned on the quote above) will start counting down.
Unlike walls, if a lighthouse has been fully corroded, it leaves no base or stump in place. It completely disappears as it has never been built before, and the price in coins for its reconstruction would have to be fully paid.
To try and avoid the corrosion of the building, Monarchs can upgrade the lighthouse. Lighthouses strengthened with better materials will have a longer lifespan.
So, after it has been built as a wooden lighthouse, the structure can be upgraded to stone for twelve additional coins, and finally to iron for eighteen additional coins. The stone and iron upgrades requiring respectively the stone and the iron technologies.
Just like when it was built, the lighthouse is upgraded instantly, without the need of builders.
When arriving at an island with a lighthouse of any tier, the boat will arrive, intact, at the far side dock.
The existence or not of a lighthouse on an island can be spotted on the map. If the island has a lighthouse on its cape side, the icon of the building appears on the chart of that island. On the chart of all islands the lighthouse symbol appears on the right side of the island illustration, except for the fifth where it is shown on the left side.
And the icon should show the tier of the lighthouse as indicated on the table on the right.
If there is no lighthouse icon on the map, then there is no (or no longer a) lighthouse on the island, either because it has never been built, or because it has decayed when the Monarch was away from there.
For more than two years since the game release, the community tried, without success, to understand the purpose of the upgrading the lighthouse. Finally on May 2021 the developer Alan Kertz shares a relevant chunck of information about that: 
“ Let me clear it up:
- All Lighthouses give 100% chance to land at the Lighthouse when you return to an island. If you have no Lighthouse you have 100% chance to crash the boat and need to build it again.
- Each tier of Lighthouse has a higher decay resistance. It takes longer for them to break down. They do decay over time, and if when you return to an island and the light house is decayed: you crash the boat.
- Lighthouses will only decay if there are no walls present on the island.
That's it. It does not affect other items in the Kingdom.
- Developer Gordon in a in which they showcased the game, on 6 December 2018, just a few days before the release.
- Safe landing on the third island with a stone lighthouse on 1.0.1). (Two Crowns v.
- As seen in these videos: 1.1.3 and 1.1.10 respectively). and (Two Crowns v.
- The community efforts are recounted on this user blog post.
- Developer Alan Kertz, 3 May 2021 on .