The big mistake is treating Lina like a normal lane bully you can just outlast. She is usually strongest when you trade small bits with her over and over. If you can, pick a mid that can either threaten her bottle control, punish her low armor, or clear waves safely without walking into constant right-click pressure.
In lane, the goal is not to beat her at her own game. Keep the wave in a spot where she cannot freely hit you and the creeps at the same time. If she takes the lead, stop bleeding resources trying to contest every creep. Go for efficient, boring CS and protect your HP for rune fights and rotations. Once she gets travel boots or a big damage item, she turns every overextended lane into a kill lane, so vision on likely rotation paths matters a lot more than people think.
Also, she tends to feel way worse when your team has no answer to her after lane. If nobody pressures her towers or forces her to show defensively, she gets to keep the map open and just pick off isolated heroes. That is where the game usually slips away.
NimbusLatch:
The wave control bit is huge. A lot of mids try to stand in front of her and just lose the lane by inches until they cannot step up anymore.
CedarBlink:
Yeah, and if you are behind, it is usually better to drag the wave or reset it than to keep taking bad hits for one ranged creep.