  Ramanujan presented four identities for third order mock theta functions in
his Lost Notebook. In 2005, with the aid of complex analysis, Yesilyurt first
proved these four identities. Recently, Andrews et al. provided different
proofs by using $q$-series. In this paper, in view of some identities of a
universal mock theta function \begin{align*}
g(x;q)=x^{-1}\left(-1+\sum_{n=0}^{\infty}\frac{q^{n^{2}}}{(x;q)_{n+1}(qx^{-1};q)_{n}}\right),
\end{align*} we establish new proofs of these four identities. In particular,
by means of an identity of $g(x;q)$ given by Ramanujan and some theta function
identities due to Mortenson, we find a new simple proof of the fourth identity.
