According to the invention, there is provided a novel romaine lettuce cultivar, designated CVX-35. ‘CVX-35’ is described as a vigorous romaine cultivar recommended for the main lettuce growing regions of California and Arizona. It has larger frame size and heavier weight, short core length, savoyed and glossy leaf color, corky root rot resistance, Bushy Stunt virus resistance, no fringe burn on mature leaves and also yellower heart leaf color. The present invention relates to a new and distinctive cos or romaine lettuce (Lactuca sativa L.) variety designated CVX-35. This invention thus relates to the seeds of lettuce cultivar CVX-35, to the plants of lettuce cultivar CVX-35, to plant parts of lettuce cultivar CVX-35, to methods for producing a lettuce cultivar by crossing the lettuce cultivar CVX-35 with another lettuce cultivar, and to methods for producing a lettuce cultivar containing in its genetic material one or more backcross conversion traits or transgenes and to the backcross conversion lettuce plants and plant parts produced by those methods.