Usually LCD displays come in a plastic "cage" that has pins (more precisely, bumps - they are very short) on each corner of its back. The PCB has holes to fit in, but that's just to prevent the display from sliding horizontally on the board. The board is then attached someway (screws, etc.) against the case "top" which has a window for the display, a little smaller than it in each dimension, and that holds it in place. Usually there's no need for an adhesive or glue, which also makes repair easier; just the LCD ribbon is really mechanically attached to the board. But for hobby projects there's nothing that prevents you to do so.
There are other, less popular methods. Displaytech's "LCD Connection Methods" document has a few diagrams, but it's not possible to attach a file here in .pdf format. In a roundabout conversion method, it's now on E&R's imgur account here, sorry for the low quality.
No great risk compared to original condition as long as
Lithium Ion batteries are prone to "vent with flame" type sudden 'self-dismantlement' if subject to heavy discharge or if the battery casing is ruptured or penetrated by a sharp (or other) object.
'Vent with flame' is not quite an explosion, but the difference is sometimes hard to spot - especially if you are standing close by, or you bag is in an aircraft overhead locker at the time, or inside your laptop :-(.
The following are examples of what could go wrong.
All are very unlikely, but Murphy loves a challenge :-).
ie this is "no biggie", it should be easy to repair but DO do it properly as there is a small but finite change of "interesting outcomes" if you don't.
If contact between two parts not intended to come in contact can occur the aboVe can apply.
If you left a slit between the two halves that eg a steel ruler could slide into when both were in a bag together then the above could occur.
If there was the opportunity for bits of foil (off candy or medicine etc) or a small coin to penetrate then the above can occur.
If you dropped the battery and the case was able to re-separate under impact so that the batteries moved, then the above can occur.
Likley? - No.
Interesting if it does? - Very.
You don't say what the battery pack is out of. If it's like a cellphone or laptop it may clip or slide into a present battery holding location and making it fatter with tape or ties may cause it not to fit. Worse, if you use thin tape or ies it may cause the battery to jam. Levering a LiIon battery out of something is better avoided if possible.
So - you say "glue together".
How was it joined before? If their glue failed, why should yours last?
What is it made of? How long will your glue last?
If you can use a mechanical method that is easy and works well, consider using it.
Super glue (cyanacryloate) is good for positioning and quick tacking but has an unknown long term result with unknown plastics. Silicone rubber works for most plastics but has long pot life. Using the two together (on different locations on the case for each) gives you fast set and the long life of silicone rubber.
If the case was ultrasonically bonded originally, as has been suggested, it may be hard to glue (or not). Murphy says that if they did not need to glue the plastic there is a moderately good chance that they chose one that is hard to glue for whatever reason.
One option, usually not pretty but which can be effective, is to heat seal the two parts back together with a soldering iron or other suitable hot tool. You can also get specialised plastic welding tools which are (understandably) well suited to this task. Care needs to be taken not to overheat the batteries or to slip and insert a conductive iron tip into a suitably unfortunate location. Given due care this can be a good solution.
Play, Report. Enjoy
Best Answer
It's not clear whether you want to attach LEDs to the exterior of the enclosure or have them mounted in holes in the aluminum. Typically you would mount them in holes, and to secure them properly, you should consider an LED mount:
At left shows how the LED is secured in the housing. At right shows the mount components separately. It's just a plastic holder which is held in place with a ring.
Look for "LED mounts" at your electronics supplier, there should be a variety to choose from to fit your LED and enclosure thickness.