Yes, it was specifically stated that Tamara Price is Lani's mother.
Here is Abe and Valerie's relationship in a nutshell (from Beth's Days of Our Live's Page, which is no longer online):
During this time, however, Valerie met Sgt. Abe Carver from the Salem Police Department. Though it took a while, Abe and Valerie began dating. Valerie discovered that Abe, who seemed to be rough around the edges, was actually a dedicated man with a family not unlike hers. His father had, too, died an untimely death; he single-handedly supported his ill mother, his sister and one of his little brothers. Knowing about Abe's home life, Valerie was able to grow closer to him. In early 1982, Abe was shot while on duty. Valerie operated on him, and proceeded to spend long hours by his bedside until he recovered. But after his recovery, Valerie wanted a commitment from Abe, a commitment he couldn't promise. Hurt, Valerie broke up with Abe. She was soon offered a job at a prestigious hospital in New York City, and she accepted it. After saying good-bye to Danny and David, Valerie moved to New York.