Your reasoning appears to be valid, and this is typical non-Ohmic behavior for an incandescent light. Non-Ohmic meaning a non-linear relationship between voltage and current.
Initially, as the potential difference across the filament is increased, so to does the current inside it and energy is dissipated as heat. This results in the filament operating at a higher temperature. But as you have also pointed out, the temperature increases, which results in the resistance of the filament also increasing.
If we have a look at the current-voltage current graph for such a process, we get something like this:
Although the graph you drew was voltage versus current, it is similar to this which shows current versus voltage.
Such non-Ohmic behavior results because of the heat generated by the filament in the lamp.
For a lamp powered by a normal battery, for example a torch, such a power sources provides (nearly) constant voltage.
When first turned on, the incandescent lamp starts with a relatively low resistance, like a few Ohms. Because of this, there will be a large in-flow of current. This means that the filament will become hot very quickly.
With this increase in temperature, the resistance rises, ultimately resulting in a reduced current as the lamp settles to its normal operation. As you have described, the lattice vibrations lead to an enhanced scattering of electrons which reduces the current flow.