Authentic production technique:
First you make two or three different lambics, one per year so they will be aged different amounts. Then you add a ton of raspberries to one of the beers and wait for them to ferment out. Finally, you blend beer from the various batches (getting sourness from the older ones and fermentable sugars to ensure bottle carbonation from the younger) and add a bunch of non fermentable artificial sweetner to make sure it will still be sweet even after bottle conditioning.
Not an easy process!
If you don't have two to three years to put into this, you could try making a regular wheat beer, doing a secondary fermentation with raspberries, then adding both lactic acid and artificial sweetener at bottling time. It wouldn't taste the same (nowhere near as much complexity) but would at least tickle the same "fruity, sweet + sour at the same time" buds.