tl;dr On the the third roll of a 6 the players turn immediately ends.
As Ludo is a traditional game that is many 1000's years old its hard to find an official rules source.
The Wikipedia article here says-
When a 6 is rolled, the player may choose to advance a token already
in play, or may enter another staged token to its starting square.
Rolling a 6 earns the player an additional or "bonus" roll in that
turn. If the bonus roll results in a 6 again, the player earns an
additional bonus roll. If the third roll is also a 6, the player may
not move and the turn immediately passes to the next player.
Rolling the 3rd 6 means the players turn immediately ends. I couldn't find anything in any other rules to contradict that.
Wikipedia also talks about different variants-
To speed the game up, extra turns or bonus moves can be awarded for
capturing a piece or getting a piece home; these may grant passage
past a block.
As Ludo is such as old game it is not not surprising there are going to be many different variations including this rule which you used in your example. However the outcome is the same.
Here are two examples
1) Player rolls a 6. They take an action. They roll again.
Player rolls a 6. They take an action. They roll again.
Player rolls a 6. There turn immediately ends.
2) Player rolls a 6. They take an action. They roll again.
Player rolls any 6 and lands on an opponents piece. They take an action. They roll again.
Player rolls a 6. There turn immediately ends.