Is it possible to get the best ME3 ending without Live Gold membership?

Yes, you can - in the Extended Cut free DLC which updates ("fixes") the endings, the required EMS readiness was lowered to 3100 from 4000 (SPOILERS - source - Extended Cut info) and it is certanly possible to achieve the 6100 military strength points required for best endings with 50% readiness penalty just by playing ME3 singleplayer without any multiplayer or mobile game addons.

Just make sure you grab the free DLC from Xbox Live before playing.