Since I am learning assembler I have more questions. I have this code
which is suppose to append text on a variable.

Source db "",0

invoke lstrcpy, Source,"Item1"
invoke lstrcat,Source,Source

Not sure why this is not working, Source should equal "Item1Item1"

There are at least two thing to realise here.

1) Your "source" buffer is too small and you risk overwriting something else that follows it.
2) lstrcat is not a clever function. It may not work the way you expect above when your source and destination are the same. You have to check exactly how the functions operates to see what happens in this situation.