[6] In October 2001, the band conceived their fourth album, Redwood, when they were taking a break near Occidental, California, in a ranch belonging to Matt Greenhill.

[9] More stripped down and laidback than its predecessors,[11] Redwood features "highly innovative arrangements of traditional tunes" and new compositions composed by several of the band members.

[12] One biography said that, "with Redwood, the group tried hard to re-create for record what one of their live gigs was like, complete with their trademark break-neck speed interplay between the instruments and their peerless musicianship.

"[11] A rhythmic set, "the interplay between the three lead instruments as they weave in and out of the melody, brings out tuneful qualities which are not immediately apparent.

"[14] "Welcome Home" was described as combining "a Donegal jig with a sumptuous Junior Crehan tune and a jaunty new reel from Donogh Hennessy.

[11] "Spoil the Dance" is "a set of three great reels given the famous Lúnasa low whistle treatment, finishing off with Cillian Vallely's pipes rampant.

"[11] "Two-Fifty to Vigo" is a cover of the Shooglenifty track from their debut album Venus in Tweeds (1995), whilst "Temple Hill" features the band "negotiating the tricky turns of the melody at a dangerous speed.

[7] The dispute became heated and public, and almost prevented the album from being released, though the band only commented that "things didn't quite work out as planned.

"[19] The Irish Echo said the band's "heated conctractual dispute" with the label "became public and tended to overshadow the musical merits" of Redwood.

[21] Although Redwood completed the band's three-album contract with Green Linnet,[10] the band chose not to resign with the label due to the affair,[21] and instead signed to Compass Records for their subsequent album, The Kinnitty Sessions (2004), which one critic descibred as "a deliberate attempt to recreate Lúnasa’s independence and regain control over their music and recorded output.

"[23] Alex Monaghan of The Living Tradition was favourable, saying "every track in these forty-three minutes is a precious nugget" and described it as "another near-perfect CD from Ireland's best instrumental band.

"[11] Jamie O'Brien of Roots World said "the flitting of the flute, the dance of the fiddle, the flow of the pipes, the strong guitar and bass: Lunasa's lineup is not unique, but their playing is.

"[14] Craig's Music Reviews said that Redwood continues the band's successful "ability to blend traditional Irish songs with their own compositions so that the average listener cannot tell the difference between the two.

"[6] In the era, they toured the United States three times among many other places and in 2003 played a "much-covered appearance" at the Celtic Connections festival in Glasgow.

[6] That same summer they played at Quebec City Summer Festival, playing alongside such musicians as Billy Bragg, Bob Geldof, Daniel Lanois, Bruce Cockburn, Rosanne Cash, among others; the performance won the band the Coup de Coeur Miroir prize.