Why wavelength is not measured with a unit of time?
The plot you provide gives the amplitude versus time so there is no length, other than "length" of time, i.e., period) to speak of.  Without further context, what you have plotted there is a simple sinusoidal function of time, not a wave.

A wave is a function of both time and space.  For example:

$$f(x,t) = \cos(\frac{2\pi}{\lambda}x - \frac{2\pi}{T} t) $$

where the wavelength \$\lambda \$ (measured in units of length) and period T (measured in units of time) are explicit.





Often, this is written as:

$$f(x,t) = \cos(kx - \omega t) $$

where k, the wavenumber is:

$$ k = \frac{2\pi}{\lambda} $$

and \$\omega\$, the angular frequency is:

$$\omega =  \frac{2\pi}{T}$$

The wave propagates with phase velocity 

$$v_p = \dfrac{\lambda}{T} = \dfrac{\omega}{k} $$

Then we can write:

$$f(x,t) = \cos\frac{2\pi}{T}(\frac{x}{v_p} - t) = \cos\omega(\frac{x}{v_p} - t)$$

or

$$f(x,t) = \cos\frac{2\pi}{\lambda}(x - tv_p) = \cos k(x - tv_p)$$