Small cell carcinoma of the lung may produce paraneoplastic syndromes, of which ACTH and ADH are the more common subtypes. ACTH excess leads to excess stimulation on the adrenal cortex to produce cortisol, resulting Cushing's syndrome. Excess cortisol (normally a stress hormone) causes hypertension via potentiation of sympathetic stimulation on the vasculature. It can also cause hypokalemia by acting as a mineralocorticoid when in excess, saturating the ability of 11-beta-hydroxysteroid dehydrogenase (present in the renal tubules) to convert cortisol to cortisone, which doesn't act as a mineralocorticoid.
To rule out SIADH type: "Serum potassium concentration generally remains unchanged. Movement of potassium from the intracellular space to the extracellular space prevents dilutional hypokalemia. As hydrogen ions move intracellularly, they are exchanged for potassium in order to maintain electroneutrality."