D&C 63

Speaking of some of the wickedness that existed in the Kirtland area, the Lord said -

"...I, the Lord, have said that the fearful, and the unbelieving, and all liars, and whosoever loveth and maketh a lie, and the whoremonger, and the sorcerer, shall have their part in that lake which burneth with fire and brimstone, which is the second death.
18 Verily I say, that they shall not have part in the first resurrection."  (Doctrine and Covenants | Section 63:17 - 18)

In my mind, the second death are those that will be cast out of the presence of God for eternity.  Thus the use of the word "death", even though they may live in a glorious state.  Synonymous to this second death, as the Savior said, is that they shall have their part in that lake which burneth with fire and brimstone.  Thus this "lake" would also be for eternity.  Even though we know man will be punished for their sins which would be finite in nature, I believe this "lake of which burneth with fire and brimstone" will be an eternity of pondering "what could have been" now that it is too late.

But of those that are willing to harken to His will and commandments the Lord suggests that there is much more saying -

"...he that endureth in faith and doeth my will, the same shall overcome, and shall receive an inheritance upon the earth when the day of transfiguration shall come..."  (Doctrine and Covenants | Section 63:20)

Then adding -

"...now, verily I say unto you, that as I said that I would make known my will unto you, behold I will make it known unto you, not by the way of commandment, for there are many who observe not to keep my commandments.
23 But unto him that keepeth my commandments I will give the mysteries of my kingdom, and the same shall be in him a well of living water, springing up unto everlasting life."  (Doctrine and Covenants | Section 63:22 - 23)

Which suggests to me that there are yet even greater and personal things (or mysteries), if we keep His commandments, He will make known unto us according to His will that as we learn and follow His will, great and eternal blessings will follow, even exaltation.