Hi Houminer,
I would go on buying something basic that can fit for the meeting you have,
you dont need to go buy a hugo boss stuff, but a nice jean and an elgant shirt, I am sure the people you meet will understand... I estimate this
around 120$, EL-AL would probably pay you for this with no troubles.

It happend to me twice, I even had to go and buy more as it took 4 days
to my luggage to arrive, After explaining to the nice el-al represntative that
althought there is an urban legend of wearing your underwears 4 times, 1 from each direction - I have no plans to do so, I got after the first 24 hours (and the first 120$ approval) an approval for additional 130$ (Which 250$ is the maximum limit EL-AL can give).

As for making the complain, It really depends how you luggage was tagged,
If it was tagged including the OS flight, then you need to complain to OS,
If it was tagged only for the LY route, And then you had to re-checking on OS
then you complain on LY.

From my expirence with lost luggage, If you loose anything, Its better doing it on EL-AL