You can't do this without a core hack. My recommendation is use composer autoloader along with default autoloader in Magento. You can implement this either by :

1. Require composer autoloader via Mage.php

2. Listen to very first events which is generating by Magento and require composer autoloader via your observer. (more cleaner approach).

3. Put Varien_Autoload in local codepool and put your autoloader logic in that file. (Recommendation from Vinai Kopp)

You have a wonderful answer from Alex from this thread.

EDIT

Solution - 1

If you just want to autoload classes inside a particular namespace (if they are follows PSR-0 standards), then Magento-PSR-0-Autoloader will be the best option. All you need to do is, install this extension and edit your app/etc/local.xml file and put this

<psr0_namespaces>
    <DTS\eBaySDK\Constants />
</psr0_namespaces>

^{Note : However I have no past experience with this extension. I may be wrong. But play around it. I think it would be sufficient for you.}

Solution - 2

However if you really need to go on with your autoloader in your question, Then create a module and observe to the event resource_get_tablename.

File : app\code\{codePool}\{Namepace}\{Module}\etc\config.xml

<config>
    <global>
        <events>
            <resource_get_tablename>
                <observers>
                    <namespace_module>
                        <class>namespace_module/observer</class>
                        <method>addAutoloader</method>
                    </namespace_module>
                </observers>
            </resource_get_tablename>
        </events>
    </global>
</config>

File : app\code\{codePool}\{Namepace}\{Module}\Model\Observer.php

<?php
class Namespace_Module_Model_Observer
{
    const AUTOLOADER_FILE = 'path/to/your/autoloader.php';
    public function addAutoloader()
    {
        require_once self::AUTOLOADER_FILE;
        return $this;
    }
}

Here we are observing to resource_get_tablename event because which is the very first event that is fired by Magento. In our observer we are simply requiring the autoloader file in the question. So dont forget to put the correct file path for the constant AUTOLOADER_FILE.

That will register your custom autoloader and hence Magento uses your autoloader prior to the default autoloader.

if you installed the library via composer, I can only see one potential problem on first sight.

the psr-0 namespace declaration must have (I think) a trailing backslash (which also must be escaped). So it would look like this:

"psr-0": {
    "EasyAsk\\": "lib"
}

The file for the class in your library should then be located in lib/EasyAsk/Impl/RemoteFactory.php and have the namespace EasyAsk\Impl and the class name RemoteFactory

you could also leave out the type magento2-library then which would default to the library and just use the default composer autoloading mechanism.

you can find further information on composer psr-0 autoloading here: https://getcomposer.org/doc/04-schema.md#psr-0

to see if your library is correctly loaded via composer you can also look into the file vendor/composer/autoload_psr0.php (or smth similar). There should be an entry for this.

To recompile the composer autoloading files you can execute the following command in your Magento 2 root dir: composer dumpautoload