We introduce a new pixel-based source reconstruction code built on and extending previous work in the field and explore the systematic biases and statistical uncertainties in the lens modelling of resolved background sources. Effects of pixelization inherent to the methodology of such algorithms and observational restrictions, such as telescope pointing, noise, and image resolution, are investigated. The code is also applied to observations of lensed, high redshift galaxies, which would otherwise, in the unlensed case, be unobservable. We constrain the lens model using maps of CO rotational line transitions, as well as optical and infrared data. In addition, properties of the source, such as the gas mass fraction and dynamical mass, are calculated.