The other answer solves your immediate problem, but a solution for the general case of "combining two commands" remains to be mentioned. Believe it or not, the Unix ecosystem was designed with this in mind, and your shell will definitely give you a way to do it.
If you want to feed a file through a "pipeline" of commands, you use the | (pipe) character in bash (presumably, the shell you are using).
Some other useful tools are worth mentioning here too: the "cat" utility, and the ">" redirection operator.
Let's assume your file is called input.txt, and you want to run it through your pipeline and call the result output.txt.
Let's build up our command piece by piece:
$ cat input.txt
Here's that "cat" I was talking about. For all intents and purposes, it just produces the content of your file. Now, let's add the first command in our pipeline: the "remove non-alphabet" part. I'll take a piece out of heemayl's sed command to do this:
$ cat input.txt | sed 's/[^[:alpha:]]/_/g'
Learning sed and regular expressions is a whole 'nother beast, so let's just be content that this command does what we want for now. Adding on the next piece:
$ cat input.txt | sed 's/[^[:alpha:]]/_/g' | tr 'A-Z' 'a-z'
I've taken a different approach than heemayl for this one, but it does the same job. Finally, let's put the output in the destination we want:
$ cat input.txt | sed 's/[^[:alpha:]]/_/g' | tr 'A-Z' 'a-z' > output.txt
There we go, we've done it. You can string as many commands together as you want with the | operator, then put the output in a file using >. This is a very common task in the command-line environment, so it's good to know what's going on and get used to using it. ;)