The 18-year-old from Almora notched up a comfortable 21-18, 21-11 win over Bruun in a 48-minute semi-final clash on Friday night.
Lakshya, the Asian Junior champion, will face second seed Victor Svendsen of Denmark in the finals.
The semi-final clash was a close affair initially with Lakshya and Bruun exchanging leads frequently before the Danish shuttler jumped to a 11-9 advantage at the break.
However, Lakshya erased the deficit after the interval and build on a slender 13-12 lead to slowly move ahead and eventually pocketed the opening game comfortably.
Lakshya came out with all cylinders blazing in the second game to jump to a 6-2 lead early on and then reeled off five straight points to grab a 11-3 lead at the breather.
The Indian produced another burst of five straight points to create a huge gap which Bruun failed to bridge.