The 'Fear' star is a big fan of the reformed Britpop legends but believes her actor father Keith Allen's close friendship with bassist Alex James contributed to the group's rows.
Blur parted ways in 2003 but the rockers - Alex, frontman Damon Albarn, guitarist Graham Coxon and drummer Dave Rowntree - reunited earlier this year and announced the would perform a series of shows.
She said: "I love Blur. I was a bit dubious about Damon Albarn because my dad was on the Alex James side when they were falling out.
"I think my dad made it quite hard for the rest of Blur because he was out getting completely f**ked with Alex and I think that probably annoyed them quite a lot."
Lily also admitted she and singer Damon have not always seen eye-to-eye but she believes they have finally put their differences behind them.
She added: "Damon and I have had our ups and downs but we're friends on Facebook and I do really like him."