It took me about two minutes to read this word but I pretty quickly picked up on what it meant. The question I have is: isn´t -laş and -tır kind of double? Don´t they both mean ´to make~´ something? 

You are right! It´s kind of double but it is the preferred way when you derive new verbs.

usually -la-mak should mean to make something but

-la-ş-mak = to become something

-la-ş-tır-mak to make something become (something like that)

Maybe this is a good example

Onu uzaklaştırdım - I made him move away

uzaklaştım - I moved away

you will not be able to make it a law-code-rule-norm

Certainly, it is..

There is one more thing that could be added to this..

-la.ş.(mak) doesn´t always mean "to become"

-ş also indicates that the action is done by more than one person and often directed to each other.

Here is an example:

kucak -- (noun) bosom

noun + la => verb

kucakla

arkadaşını kucakla - hug your friend

verb + ş => verb (cooperative-reciprocal voice)

kucaklaş

kucaklaştılar - they hugged eachother

verb + d/tır => verb (causative)

kucaklaştır

onları kucaklaştırdım - I made them hug eachother