My lawyer = مُحاميَّ
If it is hard, one can say also (my personal lawyer): المحامي الخاص بي ... for example
This may be an issue of font, but it looks to me like the لْ in 'al' and the مُ in 'muHaamii' are on top of each other, or else elided into some other character that I'm not (yet) familiar with. Is this how it's supposed to be written?
Yes it is just a font thing. In Arabic calligraphy in general sometimes the Meem م can be written like that when coming after AL or written as a complete circle. Change the font if you can and see, it might change in shape as well.