Well, Sairie, if you're not BF, then yes, a lie in is technically possible. But usually you'll hear the baby cry (they're theoretically in your room until six months) and once you've heard them yell, be fed, have their bum changed, blah blah blah, you're awake. I was BF in any case.
But even once I stopped BF, DH would go in to see DD when she wakes (that's our deal - he's better at mornings than me) and she wanted me. When she was quite small (say 9-12 months) she'd try to wriggle out of his arms and crawl to our room. Sometimes DH would manage to distract her and get her downstairs and sometimes I would go back to sleep (I'd always have heard the howl of "COME AND GET ME I'M AWAKE NOW"). But rarely. Our solution has always been for us all to sleep at lunchtimes on weekends when she does. I don't mind the lack of lie ins as I wasn't a big lie in person before anyway. But we've had a couple of weekends away without her and it's been GLORIOUS to sleep to 9 or 10. Wonderful.
So I guess depends on how good you are at getting back to sleep. How quick your OH is to get up and deal with said child. And how much the child wants you (over your DH/DP).
In our case, DH was doing a part time masters on top of his day job for the first two years of DD's life so was only around 7-7.45am. 7 days a week. and 6-7pm on weekends. So she didn't really trust him and know him. Not his fault - an unavoidable outcome of the situation - but she only wanted me. Now he's around a lot more, she will be more likely to accept daddy, but still wants me, particularly if she's sad. But then I'm a SAHM, so I'm her constant.