If iam adding a music/ soundtrack(music only no lyrics) to a video would it be haraam?
First of all listening to music is itself a sin. It is second thing that you are going to add lyrics. You are going to help promote the music in this way. Its bigger than listening to music because you are going to promote a sin.
Imraan Bin Husain (radhiyallahu anhu) narrates that Rasulullah (sallallahu alayhi wasallam) said: "In this Ummah will be earthquakes, disfiguration (of faces which will be transformed into apes and pigs) and showers of stone (descending on them from the heaven)." A man from among the Muslimeen said: "O Rasulullah! When will this be?" Rasulullah (sallallahu alayhi wasallam) said: "When singing girls and musical instruments will become profuse and when liquor will be consumed (in abundance)."(Tirmizi)
The words from hadees e Nabwi SAWW. So if music is a sin then adding lyrics is promoting a sin and participation in a sin is also a sin.
As long as music doesn't promote something against the teachings of Islam it's permissible. What I say is based on the opinion of other scholars not just my own opinion. This is a complicated matter but you are free to choose the one you like, since there are scholars for both sides.
Imam Ghazali said there are 3 types of music:
1) The one that emerges illegitimate urges and desires in you, which is completely Haram.
2) The one that has no harm but becomes Makruh because you give most of your time to it and it prevents you from doing useful work.
3) The one that has no harm, emerges good intentions and makes you relaxed, which is Halal.
Some reading about it: http://www.dar-alifta.org/Foreign/ViewFatwa.aspx?ID=4866
Allah knows the best !