LESS mixin a variable class name

There are at least 2 problems with what you are trying to do (for LESS >=1.6 see update bellow):

1) Unfortunately it is not possible to call a mixin using selector
interpolation.

With selector interpolation LESS expects the construct to be of
following format:

.@{selector-string} { property:value; }

(the interpolated selector can have also some static string pre or
post the interpolation)

so

.@{selector-string};

is Unrecognised by the LESS compiler. See more here:
How can I call a mixin by reference in LESS?

2) A ruleset with an interpolated selector gets directly printed to the CSS output and does not exist as a mixin that you could reuse in the LESS run

For example:

@foo: test;

.@{foo} {
  length: 20px;
}

.bar {
  .test;
}

will return:

    Name error: .test is undefined
    .bar {  .test;}

See more on that here: LESS CSS: Reuse generated .@{name} class as a mixin

Possible solution for your problem would be redifinig the font awesome rules as some kind of reusable mixins (without using interpolation). Something like this:

@fa-var-github: "\f09b";

.fa-mixin() {
  display: inline-block;
  font-family: FontAwesome;
  font-style: normal;
  font-weight: normal;
  line-height: 1;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
}
.fa-mixin-lg() {
  font-size: (4em / 3);
  line-height: (3em / 4);
  vertical-align: -15%;
}
.fa-mixin-icon(@icon){
  @var: "fa-var-@{icon}";
  &:before { content: @@var; }
}
i {
  .fa-mixin;
  .fa-mixin-lg;
  .fa-mixin-icon(github);
}

If you don’t really need the variables and just want to include the rules, the best way would be just to import the compiled CSS version of the FontAwesome (see answer here):

@import (less) 'font-awesome.css';

and then you can just use the CSS rules like LESS mixins or extend their selectors as you see fit and it should work perfectly.

---

Update:

As of LESS >= 1.6 rules with interpolated selectors can be accessed as mixins … so the #2 limitation form above does not apply anymore (but you still can not call a mixin dynamically with interpolation). So you can simply call LESS mixins and variables from the imported font-awesome.less file like so:

i {
  .fa;
  .fa-lg;
  &:before{
    content: @fa-var-github;
  }
}