Citing from Wikipedia:
For an Itô drift-diffusion process $$dX_{t}=\mu _{t}\,dt+\sigma _{t}\,dB_{t}$$ and any twice differentiable scalar function $f(t,x)$ of two real variables $t$ and $x$, one has $$df(t,X_{t})=\left({\frac {\partial f}{\partial t}}+\mu _{t}{\frac {\partial f}{\partial x}}+{\frac {\sigma _{t}^{2}}{2}}{\frac {\partial ^{2}f}{\partial x^{2}}}\right)dt+\sigma _{t}{\frac {\partial f}{\partial x}}\,dB_{t}$$
The important part to notice here is that $\mu_t$ and $\sigma_t$ are deterministic functions, namely, they depend (possibly) only on $t$ but not on $B_t$ (as pointed out in the related Wiki page).
Question. Is Ito's lemma applicable to the Langevin equation? $$ dY_t=aY_t d t + b\,d B_t, \qquad a,b\in\mathbb{R} $$ (here $Y_t$ is the velocity process and $dB_t=\Xi_tdt$, where $\Xi_t$ is a white noise).
Apparently, it can't, for in this case $\mu_t=aY_t$ is not deterministic. So either Ito's lemma does not require $\mu_t$ and $\sigma_t$ to be deterministic, or something else which at this point I don't know.