Apply Axiom of Induction:

If $n=2^{k+1}$ and $k>1,$ then:

$T(n)=2T(\frac{2^{k+1}}{2})+2^{k+1}$

$=2T(2^k)+2^{k+1}$

$=2(2^{k}lg{2}^k)+2^{k+1}$

$=2^{k+1}((lg{2}^k)+1)$

$=2^{k+1}lg{2}^{k+1}$