I just found out that getting the transformation matrix is possible using 
some more low level part of the sage interface (i.e. use the ntl wrapper 
directly).


sage: B=ntl.mat_ZZ(5,5,range(25))
sage: B.LLL(return_U=True)
(2, 1250, [
[1 -2 1 0 0]
[2 -3 0 1 0]
[3 -4 0 0 1]
[1 0 0 0 0]
[-3 1 0 0 0]
])


return_U is the keyword argument that also gives you the transformation 
matrix

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