The pulp and paper industry has an important role in the industrial transition towards net zero or negative emissions, given its renewable biomass-based feedstock and energy supply. In particular, pulp and paper mills have large existing sources of biogenic CO2, with a high potential to contribute to carbon dioxide removal through carbon capture and storage (CCS). To effectively navigate anticipated changes in feedstock and energy markets, there is a need for a better understanding of how different technology pathways for the pulp and paper industry interact with one another, for instance, how enhanced valorization of biomass side streams may affect the potential for carbon capture. This paper aims to investigate the effect of combining carbon capture with lignin extraction in a chemical pulp mill. Pinch analysis is used to study how the targets for heat recovery, fuel usage and electricity generation, are affected by different mill and capture configurations. Based on these results, the effect on carbon flows is evaluated. The results show that when carbon capture technology is implemented and fuel use is minimized at the case-study mill, there is still enough heat available from the recovery boilers to supply the process needs without requiring usage of a utility boiler. However, when carbon capture is combined with lignin extraction, the heat production of the recovery boilers is no longer sufficient to cover the process demands, and additional heat from a utility boiler is required. However, this case implies that some of the carbon leaves the mill embedded in the extracted lignin product, which can be expected to have a higher value than captured carbon dioxide. When back-pressure electricity production was maximized for the different mill configurations, a very high fuel-to-electricity efficiency could be achieved, but since the CO2 emissions from the utility boiler were not assumed to be captured, this would lead to more carbon being emitted compared to the capture scenarios with minimized fuel use.