The Bible translation you are referring to is called the American Standard Version [ASV] which was published in 1901 as a result of a copyright agreement with the Revised Version translation committee.
In 1881, when what was called the Westcott and Hort NT text was published, it was decided to revise the KJV which was based on an inferior text. The Revised Version Translation Committee was made up of British and American scholars. During the course of the work certain minor disagreements arose as to the way the translation should proceed. On the one hand the Americans were more radical than their British counterparts who wanted a minimalist revision that kept as close to the KJV as possible.
The Americans saw themselves as bringing a fresh approach to the traditional renderings of the KJV. One of the areas of disagreement was the use of Jehovah in the OT as consistently as possible, whereas the British revisers wished to keep to the traditional LORD. It was agreed that when the British edition of the Revised Version [RV] was published in 1881 the Americans would hold off from publishing their version till twenty years had passed. This term expired in 1901 when what is now referred to as the ASV was released.
In 1944, after 43 years of ownership, Thomas Nelson sold the masthead for publication of this version to the Watchtower and since then the Watchtower edition of the ASV was very popular. In 1950 the Watchtower embarked on its own version of the NT which was released as the NWT of the Christian Greek Scriptures.
The rank and file at this time would rip out the NT section of the ASV and bind it together with the NWT NT so that they had a continuous version that used Jehovah in both the NT and the Old.
In 1960 the Lockman foundation then purchased the rights to publish the ASV and promptly began a revision. This soon came to be known as the NASV and this is without doubt the most scholarly translation from a conservative, literal point of view. It is still selling very well and is second only to the NIV in world wide sales. The NASV reverted to the traditional use of LORD in the text basically because the word "Jehovah" which is neither Hebrew nor English, being a mongrel hybrid, does not represent any advancement in theological studies.
In 2001 the NASV was itself revised and since it was only available on the World Wide Web, it is come to be known as the WEB translation. Which is an acronym that can also stand for World English Bible. This latest version of the ASV uses Yahweh in the text of the OT. It can be downloaded for free from various sites such as E-Sword.
The Watchtower no longer possesses the copyright to the ASV and it can itself be downloaded from different sites.