Electrical impedance tomography (EIT) has been employed in the field of medical imaging due to its cost effectiveness, safety profile and portability, but the images generated are relatively low resolution. To address these limitations, we create a novel method using EIT images to generate high resolution structurally aligned images of lungs like those from CT scans. A way to achieve this transformation is via Cycle generative adversarial networks (CycleGAN), which have demonstrated image-to-image translation capabilities across different modalities. However, a generic implementation yields images which may not be aligned with their input image. To solve this issue, we construct and incorporate a Mutual Information (MI) constraint in CycleGAN to translate functional lung EIT images to structural high resolution CT images. The CycleGAN is first trained on unpaired EIT and CT lung images. Afterwards, we generate CT image pairs from EIT images via CycleGANs constrained with MI loss and without this loss. Finally, through generating these 1560 CT image pairs and then comparing the visual results and quantitative metrics, we show that MI constrained CycleGAN produces more structurally aligned CT images, where Normalised Mutual Information (NMI) is increased to 0.2621+/- 0.0052 versus 0.2600 +/- 0.0066, p<0.0001 for non-MI constrained images. By this process, we simultaneously provide functional and structural information, and potentially enable more detailed assessment of lungs.Clinical Relevance— By establishing a structurally aligning generative process via MI Loss in CycleGAN, this study enables EIT-CT conversion, thereby providing functional and structural images for enhanced lung assessment, from just EIT images.