Combining two businesses in one LLC
Technically, you can run as many businesses as you like under one LLC. To move an existing business under a different LLC you would need to consider what this business actually is and/or has.
For example, if the business owns registrable assets (like real estate or vehicles) then you would need to reassign those assets from one LLC to another. This could be a taxable event since you are moving assets between entities, and such transaction needs to be registered correctly.
Another example is contracts you made with third parties on behalf of the old LLC (such as office lease) - those contracts need to be revisited and reassigned to the new LLC.
There could be many other smaller changes to be made in order to complete the transfer of the business from one LLC to another (consider as an example changing the ownership of your domain names to reflect the new company name on file with your domain registrar). I would advise you to consult an attorney and/or a CPA on issues such as reassignment of assets, contracts and other legal questions, and then make a list of all small changes you need to make to complete the process.
Just keep in mind that when both of your businesses end up under one LLC they both share each other's risks and liabilities.