The short answer is yes. Before we start, the scientific name for "lye" is "sodium hydroxide". These both mean the same thing. Now in the process of making real soap, lye is always used in the manufacturing process. Whether that's liquid or bar form.
Lye is used to turn your base oils into soap, the process where this takes place is called saponification. This is critical when turning oils and lye to soap.
One question or concern a lot of people have is with the final manufactured soap. It makes sense why there are questions of lye being in the final product of soap. To understand this concept we need to understand the science of it. Lye is used to saponify the base oils you use and turn them to soap. A proper soap will not contain any oils or lye in the final product. The lye makes the oil disappear and the oils make the lye disappear, they are the two ingredients that are used to make one final product "soap".
If you are making your own soap is is up to you if you want to add lye or (sodium hydroxide) to your ingredient list. It is really based on preference. Some people like to include all ingredients ever used to make their soap. And some may prefer to not include lye because there is not any lye in their final product.
To boil it down, there is no lye left over after a soap is properly made.