Hi Chrysalis, sorry no-one's replied to you yet. Unfortunately, we don't have any lincolnite PPEists on here so there's no one that can answer any specific questions about studying it at Lincoln. All I can tell you, is that usually about 10 students are admitted, which means that the PPE crowd at Lincoln is quite big. Lincoln is just as competitive as all the other colleges - if you're good enough to get in, then you will get in (if Lincoln can't take you, they'll make sure another colleges does) and if you're not good enough then you won't - it's as simple as that and is the same as other colleges. It's a bit pointless making an open application if a) there is a colege you like the look of or b) there is a college you really wouldn't be happy at. It won't help your chancs in anyways, as like I said if Lincoln were to be over-subscribed with very good applicants, then people will get sent to other colleges anyways, so if you like the look of Lincoln, just apply. I assume you've already looked at the following:
http://www.lincoln.ox.ac.uk/content/view/471/91/Which is the PPE page on Lincoln's website.
Regarding the college itself, Lincoln's atmosphere is apathetic and fairly relaxed with a good work-play balance - we're not as work crazy as Merton, but we have done well in the Norrington Table for the last few years, especially for a small college, so like everywhere at Oxford, we do work hard. However, we have active sport/music/drama societies and people don't work all day! To give you an example, this term I'm in 2 plays, writing for a science magazine and am also involved in the production aspect of an opera. Other ppl I know, play netball and sing in the college choir and someone I know rowed for Oxford & Lincoln, was a member of the Oxford Air Squadron, regularly went on Business trips (he also has his own business) and still got a first (but he is immensely clever)! So it's easy to have a good work-life balance and still come out with a good degree.
Hope some of that helps! Good luck with your application!