I would like to use mpl::lambda in nest.

In this case works fine.
---------
typedef boost::mpl::lambda<boost::mpl::max<boost::mpl::_1,boost::mpl::_2>
> my_max;
typedef boost::mpl::fold<
boost::mpl::vector_c<int,1,7,0,-2,5,-1>
, boost::mpl::int_<6>
//, boost::mpl::max<boost::mpl::_1,boost::mpl::_2>
, my_max
>::type r2;

BOOST_MPL_ASSERT(( boost::is_same< r2, boost::mpl::integral_c<int, 7> > ));
---------

However

---------

typedef boost::mpl::lambda<
boost::mpl::fold<
boost::mpl::_1
,boost::mpl::front<boost::mpl::_1>
,my_max
>::type >::type my_max_types;

typedef my_max_types::apply<boost::mpl::vector_c<int,1,7,0,-2,5,-1>
>::type r3;

BOOST_MPL_ASSERT(( boost::is_same< r3, boost::mpl::integral_c<int, 7> > ));
///error => becomes boost::mpl::integral_c<int, 1>
---------

How to define such nest lambda in mpl?

Uh, I see a red flag in that you don't grab the nested type typedef from your mpl::lambda invocations, i.e., I think you should have

typedef mpl::lambda< mpl::max< mpl::_1, mpl::_2 > >::type my_max;

Incidentally, you could also do

typedef mpl::quote2< mpl::max > my_max

(Well, assuming mpl::max doesn't have some hidden default parameters...)

Without grabbing the type typedef in your mpl::lambda invocation, your use of mpl::_1 and mpl::_2 are "exposed" to premature substitution.

- Jeff