Are lawyer costs which I made with respect to the alimony I need to pay to my ex-partner tax deductible?

The costs you have made to keep the alimony which you have to pay to your ex-partner as low as possible are not deductible. These are your own costs. Your ex-partner however can deduct the costs he/she had to make to keep the alimony as high as possible.

Difference is that costs made to gain income can be deducted, while costs made to prevent income loss are not deductible.