An academic lineage, or academic genealogy, is similar to a family tree for scholars, except that the scholar's "parent" is his or her dissertation advisor. There are a number of sources for this information: 1. The dissertation itself, 2. the CV, 3. a published version of the dissertation, and 4. biographical sources.
You'll see that the adviser is listed in entries for dissertations written since the late 90s or so. Be aware that names can change, so try searching variations to be sure you're not missing it.
If the full text of the dissertation is available, you will also see the dissertation adviser listed in the beginning of the dissertation.
For scholars who are still active, you may be able to find a curriculum vitae that lists the dissertation adviser. These are usually posted on the academic department's website.
Even if the dissertation is not available online, often a portion of the dissertation has been published as a journal article or adapted into a book. Typically, the author will acknowledge his or her dissertation advisor in this adapted form of the dissertation, so the next step is to find the full text of this article or book.
As you trace the lineage further back in time, it may be possible to find biographical information about scholars that indicate advisers and other intellectual influences.
While there are some online projects for compiling academic lineages, not all genealogies have been checked for accuracy.