Data-flow analysis problem adjust to Ullman-Aho's framework?
Checking initialization: Yes, you can use this framework.  You need only a single boolean for each variable.  The lattice is $V\to \{\bot,\top\}$, i.e., $2^V$, where $V$ is the set of variables. The height of this lattice is $n+1$ where $n=|V|$ is the number of variables.  The transfer functions are monotonic.  Consequently, you can use the framework.

Range computation:  No.  The lattice of ranges has infinite height.  Consider, e.g., the sequence of ranges $[0,0]$, $[0,1]$, $[0,2]$, $[0,3]$, and so on: it never ends.  Consequently, you need something more, such as widening operators.

Common subexpressions: I don't know of any nice way to express this in that framework (though there could always be something I'm not aware of).