Extend redstone signal maintaining signal strength

You can use repeaters and comparators to change the strength of a signal (reset to 15 and subtract respectively).

Signal going in the back of the repeater is increased to level 15 strength on the wire piece in front. You could put repeaters branching of a trail of wire from the target, each on activating 1 lamp. (This may require spacing the lamps.)

Comparators set to subtraction mode can reduce signal strength (read here for more info).

Comparators output the same signal strength, that they received with a two tick (1 redstone tick) delay. To extend the signal you can could just build a long chain of comparators. But this will create a long time of delay, depending on the distance the signal has to travel.

Alternatively you can save on comparators and use a chain of comparator, solid block, redstone dust and a solid block again. Repeat this as many times as you need.

You will still have some delay, but only a quarter of that of the first method.

Comparators maintain signal strength. You can use a comparator line as IceFreez3r suggested. The comparator line can be made instant using some tricks:

When a comparator is updated (for example when you power it), it calculates the signal strength it should output. If this calculated signal strength differs from the one it is outputting currently, it will schedule a so called tile tick.

This tile tick is simply a way the comparator can ask the game to execute some behaviour later, in this case 2 game ticks (1 redstone tick) later.

When the tile tick is processed, that is, after the 2 game ticks have passed, the comparator calculates the output signal strength again based on the current inputs and finally outputs it. This signal strength can be different from the one the comparator calculated before scheduling the tile tick and, in fact, it often is.

This the reason comparators do not react to signals from observers or 0-tick generators. By the time the comparator actually tries to change the output the signal is not there.

However we can use this to our advantage: If we update the comparators in our line in order using, for example, observers, and then supply the signal we want to transmit we can get an instant comparator line. Here the output that is calculated at first differs from the one that is finally used too.

So normally you would have first comparator register your signal, wait 2 game ticks, send it to the next comparator and so on, having each comparator add 2 game ticks to the delay. In the instant comparator setup, all comparators are updated in the first tick, then all wait 2 game ticks, and then they pass the signal throughout the third tick. (The comparators all fire in the same game tick, but nevertheless in order.)

Alternatively, you could, of course, also convert the signal to binary as others have suggested.

you could try converting signal strength to binary and converting it back to signal strength

you can use this tutorial for a so called "redcoder". The only thing you need to change is to repeat the patern to be 15 long instead of 8, and change the item frame for the target block. then you can wire the 15 outputs to where ever you need.