Learn Swedish: Det är viktigt att motivera löneförhöjningen. - It is important to justify the pay rise.

It means both! While motivera can mean "to motivate" (giving someone the drive to do something), in professional or formal contexts it very frequently means "to justify" or "to provide the underlying reasons for" a decision, like a pay rise.

We are currently learning to drop the word att before infinitives. Why is it kept here before motivera?

You drop the infinitive marker att after semi-modal verbs like törs (dare to) or brukar (usually do). But here, the infinitive motivera isn't following a modal verb; it's following the adjective phrase Det är viktigt (It is important). When linking an adjective phrase to a verb this way, you must keep att.

How is the long word löneförhöjningen built?

It's a compound noun made of lön (salary/pay) and förhöjning (increase/rise). Notice the linking vowel -e- joining them together into löneförhöjning. The -en at the very end is the definite suffix, making it "the pay rise".

Could I use the word rättfärdiga to mean "justify" here instead?