2 Corinthians 5:14-15

 2 Corinthians 5:14-15 For the love of Christ constrains us because we have judged this, that One died for all, therefore all died; / and He died for all that those who live may no longer live to themselves but to Him who died for them and has been raised.

In this verse, Paul does not speak of living for the Lord, by the Lord or with the Lord; instead, he speaks of living to the Lord. To live to Christ is to take Him as the aim of our living. In everything we do - at home, at work, or in the church life - Christ should be our unique aim.

 Galatians 2:19 I through law have died to law that I might live to God.

To live to law means that we are under the law, led by the law, ruled by the law, and obligated to follow the law. To live to God or to the Lord means that we are under the leading and constraint of the Lord to fulfill His demand and to satisfy and accomplish His desire.
(Truth Lessons - level 3,vol 3, p.78)

We must understand the difference between living for Christ, and living to Christ. To Christ implies that we are the Lord's possession, that we already belong to Him. For Christ, implies that we are still our own and are according to our pleasure and convenience.

We may be active and aggressive for the Lord in a natural way, doing things for the Lord by our natural aggressiveness. This offends the Lord, and distracts us from enjoying Him. Saying that we are for Him indicates that we still have things under our control and that we could leave Him.

Living to the Lord is based upon the fact that we are the Lord's. 

Romans 14:8 For whether we live, we live to the Lord, and whether we die, we die to the Lord. Therefore whether we live or we die, we are the Lord's.

To live to the Lord means that we are under the Lord's direction and control and that we desire to fulfill His requirements, satisfy His desires, and complete what He intends. (The Conclusion of the New Testiment, pp. 3215-3216)

Living for the Lord implies that we and the Lord are still two; living to the Lord indicates that we are one with the Lord.

1 Corinthians 6:17 But he who is joined to the Lord is one spirit.

All that we have, all that we do, and all that we are, are to Him; everything is wholly to Him, and now we should live to Him.

We belong to the Lord, He has paid and bought us through the great price of His death and blood. We must not forget this, and understand this. So in everything we do, it is no longer for Him since we are already His.

We have to have the ambition to live to the Lord, to be well pleasing to Him; we must be absolutely under the Lord, under His leading, restraint, and control. Everything we do must be for the accomplishment of the Lord's purpose and desire. No longer live to ourselves but live to the Lord.

(Source: Crystallization-Study of Exodus Vol 3 by Witness Lee pp. 382-383)
(Further recommended reading: Life-Study of 2 Corinthians, msgs 10, 33, 44-45)