Women's garments of 1915 were constructed with or without lining. You can check out actual patterns of the day by searching online for historic patterns. Past Patterns, for instance, sells patterns of actual period garments. Ageless Patterns is another such site. Older patterns were not as informative as modern ones but some suggest linings.
Before the outbreak of World War I, women's clothing was already becoming more simplified, with looser construction and less embellishment than during the Edwardian Era. Coco Chanel's suits of 1917 were made of jersey, a comfortable fabric most often used in the production of men's under garments.
Cotton was used in clothing construction at the time. Fabrics made of cotton included poplin, gabardine, flannel, muslin, lawn, and batiste.
To learn more about how women's garments were constructed in the early 1900s, check out some books including:
"Costume Detail: Women's Dress 1730 - 1930" by Janet Arnold
"Everyday Fashions 1909 - 1920" by Joanne Olian
"Dressed for War: Uniform, Civilian Clothing and Trapping 1914 - 1918" by Nina Edwards.