jQuery-like library for learning purposes
There is quite a performance problem with your code: it will rebuild the fn object and all its methods every time the lemon(selector, context) constructor gets called. You can avoid that behavior by using the module design pattern: 

this.lemon = (function () {

    var fn = {
    /* The code for the fn object here
        init: function (selector, context) {
            var prop = this.prop;
            ...
    */

    return function lemon() {
        this.prop = {
            collection: []
        };
        fn.init.apply(this, fn.toArray(arguments));
    };

 })();


However, you will have to add a line var prop = this.prop; in the beginning of every method of the fn object that requires prop.

Also, when introducing a new global variable, it is better for the readability of your code to use this.myVar = myValue; or window.myVar = myValue;. In fact, the var keyword should only be used for local variables.

Finally, it is often recommended to put a space between the function keyword and the following parenthesis, but that's not mandatory.