An anonymous ex-Lehman HR person tells Intern Memo what it takes to get that offer at the end of the summer:

“We do not approach the summer with a set percentage of offers that we’re looking to give out. If all 50 summer analysts perform at a high level, then we would be more than happy to give out 50 offers. The more offers we give out, the easier it is for us to fill our full-time class. It actually makes our job easier. So, in general, our interests are aligned. Lehman takes the summer interview process very seriously, because our hope is that we do not need to return to campus full-time to hire additional people. Obviously it never works out that 100% of the class receives offers, so I would venture to say that it’s more like 70%; however, that number would vary by division and year.” (emphasis added)

and also the invaluable piece of advice

“Work very hard.”

Related:
Stayin Alive A Guide for the Summer Analyst or Associate