There is a longstanding custom in Lutheran Churches, to keep a candle always lit in the east end of the church, near the altar. It is called the sanctuary lamp, or the eternal light, or perhaps other similar terms. I would offer, as food for thought, a criticism of the way in which this is practiced in many Lutheran churches. What I have in mind is the practice of having an eternal light in the sanctuary of churches that do not reserve the Blessed Sacrament.
Please note that at the top of this discussion I refer to this as a custom, and not as tradition. It does not deserve to be classed as part of the tradition of the church, and any defense of it as a respect for tradition is misguided, wrongheaded, and quite mistaken.
The Sanctuary Lamp has essentially one purpose, namely, to signify that one is in the presence of our Lord, Who is truly present in the Blessed Sacrament, reserved in the tabernacle. Such a signifying has the twin purpose of 1. honoring Christ, a sort of keeping vigil with the sacred Body of Christ, and 2. giving the faithful the opportunity and occasion to adore their Lord. In churches where the Sacrament is not reserved, it is appropriate to bow deeply upon reaching one's pew, or when crossing the center, as a way of showing reverence to the altar, the great symbol of Christ, our Sacrifice for sin. And where the Sacrament is present, it is appropriate and traditional to worship the truly present Christ by bended knee. Indeed, between the consecration and the ablutions in the Mass, this is done by kneeling. And in churches where the Sacrament is always present, traditional practice is to adore our Lord by genuflecting upon reaching one's pew, kneeling at one's place in the pew for a few minutes in prayer, genuflecting when leaving the pew to go to Communion, also when returning to the pew after Communion, upon departing, and whenever crossing the center of the church. The traditional tell tale when entering a church, as to whether the Sacrament is present, is the Sanctuary Lamp, or its absence.
In the effort of so many Lutheran churches to take a thing with which they disagreed (reservation of the Sacrament), but the external form associated with it which they apparently liked (the burning of the eternal light), and give it a new meaning, such as the presence of the Spirit of God, or the omnipresence of God, or God's eternal love, or any number of other arguments I have heard, what is really being done, surely unwittingly, is a deception. The sanctuary lamp tells those who enter its line of sight that in that space, very near that light, is the consecrated Bread of the Blessed Sacrament, which is the very Body of Christ.
The Lutheran Church, let us be clear, teaches clearly and boldly, with the Church Catholic of all its classic denominations, that the consecrated bread and wine is the very Body and Blood of Christ. By "very" I mean true, real, substantial. By it I mean exactly what it sounds like. By it I mean what the Calvinists and Evangelicals do not mean when such terms have at times been used by them in reference to their doctrine. Christ is really and personally present in the Blessed Sacrament. The Sacrament exists for basically one purpose, namely, that the faithful may be united with their Lord in the consumption of the same, for the forgiveness of their sins, and indeed, for the innumerable and immeasurable blessings of which union with Christ consist, such as strengthened faith, and comfort. That is, it is instituted for us Christians to eat and to drink. And when we do so, when we consume the Sacrament, we do not take a part of Christ away from Him, as we are crassly accused by deniers of the Sacrament, but in fact, it is consumed without ever being consumed. Thus, the fire that Moses encountered is a fitting picture in this regard. The presence of Christ is beyond all mathematics, as the Blessed Reformer stated in his debate with Zwingli. And, as he urged in his Brief Confession almost two decades later, the poetry of St. Thomas Aquinas is also helpful and clear, in that Christ, all of Him, is given to one, and to the next. Christ's presence, then, is reliable and true, before we approach the altar, and also as long as it is reserved in the tabernacle, for such reservation is practiced in many churches, even some of our own, for pastoral reasons, ie., for its consumption by the faithful.

With this doctrine of the true presence of Christ in the Sacrament of the Eucharist in mind, Lutheran churches place themselves in an awkward position when they keep the eternal light, while assigning to this eucharistic symbol a Calvinist definition or significance. Many of our churches have a eucharistic practice that is irreverent, shameful, and in short, quite fitting for a Calvinist or a Zwinglian theology. So in that regard, perhaps the empty practice of lighting the eternal light without the accompanying presence of the Sacrament is fitting after all in some of our churches.
Yet in all seriousness, Christian respect, and friendliness, I do call upon the reader to consider, or reconsider, these matters. My recommendation for those parishes and chapels that do not reserve the sacrament is twofold.
1. Consider doing so. And when you do, I encourage all the traditional expressions of reverence that have been such a healthy part of the liturgical tradition of the West. We can discuss all of those matters in due time.
2. Until you do institute the reservation of the Sacrament, extinguish the sanctuary lamp. At this point in your church, it is a practice which truly signifies nothing, that is, the absence of Christ. This is a perversity of matters. And I do not say this to insult, or be disrespectful. And if it helps your decision making process, think of all the money you will save in the mean time. And know that this discussion is not condemnation, but suggestion, and food for thought. When you keep doing things the way you've been doing it, I'll love you like a brother anyway.