If the hinge of the display of this laptop is shaky and loose, the screw of the hinge or rather the plastic around it might be broken. Cut away the lid's plastic and screw it to the bottom.
Step 1: Find a Screw and Some Tools
A small M3x16 with a nut will do on the E135 Thinkpad laptop. It's a bit bigger than the original plastic/wood-style screw and it has to. Also needed: a screwdriver PH0 (or whatever fits), 3mm drill and drilling machine. If you mix up the screws also a sliding caliper (de:Schublehre) is useful to tell which is the M2x8 screw.
Step 2: Drill
Make the hole of the metal hinge-mount 3mm big (it is, say, 2.7mm). Drill upside down, to keep the metal dust falling out of the laptop and not inside!
Step 3: Screw, Finish
Put in the screw from the bottom and mount it. cut away the excessive plastic on the lid and put all together again.