"Our" had to be removed since it is against what New Agers believe to be the 'universal fatherhood' of god. Jesus clearly states that mankind is divided into 2 camps, which is those who have the Father in common with Him, and those whose father is the devil. For the New Age "Father" is OK, but not "Our Father".
"which art in heaven"
These words define the dwelling place of our Father, namely "heaven", whereas the father and god 'of this world' is not dwelling there, as he was cast out to fall like lightning from heaven (Luke 10:18). New Agers don't believe that their 'father' (Lucifer) was cast out from heaven. Therefore "which art in heaven" was removed by the NIV editors so as not to call into question if the new age god (Lucifer) dwells in heaven or not.
"Thy will be done, as in heaven, so in earth"
By removing this line and "which art in heaven" (see above) the abode of "heaven" has been completely eliminated from the NIV Lord's prayer. The "will" of heaven simply cannot go along with the "will" of the New Age mindset.
"but deliver us from evil"
How could someone who believes that Lucifer (satan) is god, pray to be delivered from evil, it simply is not compatible with New Age thinking. Many Christians even do things because they feel good regardless of the morality involved, how then could they pray "deliver us from evil". A modern bible like the NIV cannot afford to offend its readers who do not believe in the existence of "evil".