Help optimizing this - converting 1024 byte arraybuffer to string after reversing bits in each byte

I'd consider using ArrayBuffer.map. It's something that's on arrays in ES5, but has been extended to ArrayBuffers in ES6 (and Espruino :) ).

  LCD.reverse = function (a) {
    return h.map(function(i) { 
      return (i>>7|(i>>5&0x02)|(i>>3&0x04)|(i>>1&0x08)|(i<<1&0x10)|(i<<3&0x20)|(i<<5&0x40)|(i<<7&0x80));
    });
  }

But for bit reversal you can be faster as well - there's a fun (and scary) website here full of tricks: http://graphics.stanford.edu/~seander/bithacks.html

  LCD.reverse = function (a) {
    return h.map(function(b) {return (((b*0x0802&0x22110)|(b*0x8020&0x88440))*0x10101>>16)&0xFF;});
  }

You can do it even faster with 64 bit maths (which Espruino supports) but it's something that I may be removing soon to make Espruino faster, smaller, and more JS compliant so I won't post that here ;)

Finally, you can use ArrayBuffers instead of Strings, and can predefine the code you want to add:

var preamble = E.toArrayBuffer("DIM\x00\x00\x80\x40");
  LCD.flip = function () {
    var d = new Uint8Array(this.buffer.length+preamble.length);
    d.set(preamble,0);
    d.set(this.buffer,preamble.length);
    this.i2c.writeTo(0x27,d); 
  };  

Hope that helps! I think I should probably add E.reverseByte as this comes up quite a lot. If that happens then you could be super fast and could just do: array.map(E.reverseByte)

Of course there's always the inline assembler too ;)