In a large, heavy bottom saucepan or dutch oven, stir the 2 pounds strawberries with the ½-1 cup sugar and ½ lemon. Turn the heat to medium, and cook, stirring, until the sugar dissolves.
Bring the mixture to a boil. Reduce heat and simmer for about 20 minutes; you want the jam to reduce and thicken before removing from the heat.
When jam is thickened, spoon/pour into prepared sterilized glass jars and either can or keep in the fridge for 2-3 weeks. Jam will further thicken as it cools.
Notes
To can or not to can. This decision is entirely up to you. If you predict you'll eat up your honey strawberry jam within a few weeks, skip the longer canning process and keep it in the fridge until it's gone. But, if you've made a lot of jam and wish to keep it for year-round spreading on toast, I recommend going the preserving route. It's not hard to can your jam, and you don't need any extra equipment. I've included a link to some reliable canning resources below.
Add more sugar. I've included ½ cup of sugar in the ingredients list as a starting point. Note that ½ cup of sugar will result in a jam that's on the less-sweet side, especially if your strawberries are not super sweet. You can add 1 cup of sugar for a sweeter jam, or taste as you go and add a bit more honey depending on how the jam tastes to you.
Use very ripe strawberries. This will help the jam to turn out beautifully sweet without a ton of added sugar. As noted, if the strawberries are not super ripe, you may need to add more sugar.
Puree the jam. For a smoother jam, use a masher or the back of a big spoon to smash the strawberries as they cook. This will help them break down into a smoother jam. Or, use an immersion blender to quickly blend the strawberries into a puree after they are softened. Be careful, though! The jam will be very hot.
Use the plate test. Place a plate in the freezer while the jam cooks. When it looks like it's done (coating the back of a spoon), drizzle a spoonful of jam on the cold plate. If the jam "wrinkles" and doesn't run, it's set and ready to take off the heat. If it's still pretty loose, keep cooking the jam and try again.