Most homebrew shops sell milled grain, and while uncrushed grain does store better in the long term, milled grain wil store for months or longer if stored dry and sealed well. That said, buying a grain mill is certainly a worthwhile investment for getting a consistent crush. But it isn't a necessity to shop online.
I've never had a LHBS per se. There was a local hardware store that sold some brewing supplies (dry yeast, pre-milled grain in small packages, some cleaning/sanitizing supplies, etc.), but I've always used online stores predominantly. I do typically buy hops and grain in bulk. I can't always schedule my brewdays in advance, so having ingredients on hand allows me to brew on short notice.
My only big challenge is when I want to use liquid yeast, because it is fairly perishible, so I try to use dry yeast whenever possible. If it's something where I just have to use a particular liquid yeast, then I try to schedule those brewdays in sooner rather than later once I get my order.