Using LSTMs for modelling and forecasting several time series generated by the same process
You can frame the problem this way. 

Consider each car as a sample of your dataset and use $Car^{i}$ to denote the $i^{th}$ sample. Then for each sample, you have the following features: 


Time series of cars' condition $C_0^{i}...C_n^{i}$
Other time-invariant features like colour $A^{i}$ and engine size $E^{i}$


(I am not sure how mileage fits here, do you have a time series on this as well? Intuitively mileage changes over the life of a car so it should be time series as well)

My understanding of your question is how to incorporate those time-invariant features into an LSTM model? 

Instead of only passing the $C_{t-1}$ as LSTM cell input you pass it with a vector $[C_{t-1}^i, A^i, E^i]$. Here, using Tensorflow's terminology, you input_size is 3 instead 1. $A^i$ and $E^i$ is always the same at each timestep but different across samples.