Finding a niche for the wider use of local pigs highlighted the need for information about consumer attitudes regarding pork and traditional products and the acceptability of fatter meat. With the aim to ascertain pork consumption frequency and Lithuanian consumer attitudes towards traditional pork products, as well as acceptability of traditional sausages from the meat of Lithuanian White pigs, a questionnaire-based survey and consumer sensory tests were conducted. A total of 136 meat consumers participated in the study. Respondents reported that they consume fresh or processed pork from 1 to 10 times weekly. Male respondents were more familiar with Lithuanian local pig breeds, while female respondents demonstrated knowledge of pork products. Boomer generation (1946–1964) respondents mostly (χ2 = 29.53, df = 10, p < 0.001) had pork at home compared with the respondents of younger generations. There were no significant differences in the blind sensory acceptance between sausages made in a traditional way and cold-smoked with different quantity of salt and commercial sausages of premium quality, while conventional hot-smoked sausages had lower (p < 0.001) overall acceptance. The highest (p < 0.005 and p < 0.01, respectively) acceptance for salt reduction in traditional sausages was demonstrated by the X generation (1965–1980) consumers compared with older boomer and subsequent Y (1965–1980) generations.