My commercial software is using some code source licensed under LGPL or MIT. How and where should I mention this? Is it mandatory?
I don't know the terms of the MIT license by heart, so you'll have to read it.
With regard to the LGPL: is the LGPL work you are using (hereafter referred to as "foo") a library or something else? Is the work based on foo (hereafter referred to as "bar") a derivative of foo, a work that uses foo, or are you unsure (in which case provide more info on bar)?
Generally, if foo is a library, and bar uses foo as an external dependency rather than compiling whole chunks of foo into bar, bar is a work that uses foo, and you have no particular responsibilities under the LGPL.
If you foo is a library, and bar is a modification or derivative of foo, or foo (or significant portions of foo) are compiled into bar to make it count as a derivative, the LGPL applies and you must provide the proper notices, access to the source code, etc. In this case you may at your option relicense bar under the GPL instead of the LGPL if doing so makes more sense to you.
There are a bunch of other cases, but those are the two most common.
IANAL*, but I run an open-source based development shop, so I deal with this stuff daily.
*I Am Not A Lawyer: in other words, don't take my word for it, that's what lawyers are for.
So I think you need to have this notice in your software somewhere: