My understanding is that LCD segments are almost always driven with a lowish frequency, AC (square wave) signals, which continually swaps polarity, to minimise LCD damage by DC. DC eventually destroys LCD displays by electrolysis.
That can make this harder, than it might at first appear.
You can buy individual LCD screens (seven segment), from various sources.
For LEDs, using an MCU, to read in the LCD status and then drive the LEDs. Might be the most practical solution.
In general, it is probably NOT worth spending the time, to make such a fix. But if you are learning from the exercise or the item is very important, then go ahead.
There are other possible technical challenges, further making the MCU a favourable solution. They may be multiplexed at a fairly low frequency, e.g. 5 Hz (LCDs of this type, are usually rather slow to change). Which would be too slow for LEDs, which would flash somewhat horribly. An MCU could fix that issue as well.
What gadget is this for ?