If you have a W-2 job as an employee, and you also have work (side gig, independent contractor) that is organized as a single member LLC, you can only deduct expenses on the LLC that are ordinary and necessary expenses for that particular work.
If you travel on a temporary assignment for your LLC work, you can deduct lodging and 50% of meals according to the rules in publication 463. The rule about 1 year or less for temporary relocation will be important. https://www.irs.gov/forms-pubs/about-publication-463
However, based on the way you phrased your question, you relocated temporarily because of the W-2 job. That would seem to indicate that the relocation expenses are not an ordinary and necessary expense for your LLC self-employment work. You can't use the LLC to get special tax treatment for your ordinary living expenses, the expenses must be ordinary and necessary for the LLC.
Only you know the facts. But if you did not relocate for the LLC work, then I would not try and deduct the expenses without getting professional backup from your own tax professional.
Also note, you may already know, any assistance provided by the W-2 employer is taxable, is subject to income tax and social security and medicare tax withholding, and should be reported on your W-2.
