The 'Hard Out Here' singer will be performing in Australia later this month before joining Miley for her 'Bangerz' US tour on August 1 and she plans to introduce daughters Ethel, two, and 18-month-old Marnie, to the 'Wrecking Ball' singer when her kids join her in the States.
During an interview on BBC Radio 1 today (15.07.14), Lily - who is married to Sam Cooper - said: ''I'm not going to take them to Australia.
''I'm only there for seven days and they're both under three so that would be a bit mean.
''But they are going to meet me in New York and then come on the bus with me and Miley.
''Although I don't think Miley will be on my bus, she's probably got other plans!''
Lily - who recently released her third album 'Sheezus' following a five-year break from recording - has had to get used to being a working mother since she made her pop return, but appreciates the fact she has a ''bit of money'' makes her life easier than it is for other working parents.
When asked by presenter Fearne Cotton how she balances her work and family life, Lily said: ''Probably in the same way all other working mums manage it.
''It's probably a lot easier for me because I've got a bit of money and nannies and my job's really fun. I'm very happy, very lucky.''
Lily will join Miley for seven shows starting in Uniondale, New York, and ending in St Louis, Missouri.
There are currently five separate teams working on 'Game of Thrones' projects at HBO.
She's a big fan of the band and this week she got to perform with them.