  Let $(L_n)_{n\geq 0}$ be the Lucas sequence given by $L_0 = 2, L_1 = 1$ and
$L_{n+2} = L_{n+1}+L_n$ for $n \geq 0$. In this paper, we are interested in
finding all powers of three which are sums of two Lucas numbers, i.e., we study
the exponential Diophantine equation $L_n + L_m = 3^{a}$ in nonnegative
integers $n, m,$ and $a$. The proof of our main theorem uses lower bounds for
linear forms in logarithms, properties of continued fractions, and a version of
the Baker-Davenport reduction method in Diophantine approximation.
