I believe that every reference to "hell" in the King James Bible refers to the fiery place of judgment either literally or figuratively. Do not let the figurative reference concern you. I am talking about places like James 3:6 where the tongue is said to be "set on fire of hell." I am not in any way denying a literal hell.
I usually do not refer to the Greek and Hebrew since I believe in the sufficiency of the English of the King James Bible, but perhaps a couple of comments are in order. The Greeks used the word "hades" for the abode of all dead. However, I do not find that use in the New Testament. The Bible is quite consistent in its use of the word. It means hell. The Hebrew word "sheol" can indeed refer to the grave or the pit. However, when it refers to one of these, it is so translated in the King James Bible. Therefore, when you see "hell" in the King James Bible, you can trust that it means hell.
One interesting note: you ask if "hell" always refers to the lake of fire. I am not trying to be picky, but "hell" is not the same as the "lake of fire" in the Bible. They are two different places until hell is cast into the lake of fire in Revelation 20:14. The lake of fire is evidently the "everlasting fire" that was prepared for the devil and his angels (Matthew 25:41). In fact, the beast (antichrist), the false prophet, and the devil are all cast into the lake of fire (Revelation 19:20; 20:10) before hell is cast into the lake of fire.
Hell, on the other hand, is the place of punishment for those who reject God. I believe that it is presently in the heart of the earth. It is always referred to as down (Psalm 55:15; Isaiah 14:15; Amos 9:2). It was across a great gulf from Abraham's bosom (Luke 16:23-26). When Christ died, He went to the "heart of the earth" (Matthew 12:40) for three days and three nights. For most of that time He was in the paradise where He promised to see the repentant thief (Luke 23:43).