Lidköping has no train station — the rail line that once served the town closed decades ago. The practical options are bus or car.
By bus: Regular express buses connect Lidköping with Gothenburg (around 1 hour 40 minutes) and Skövde (around 50 minutes). From Gothenburg, Västtrafik operates the route; check their website for timetables. Skövde is on the main Stockholm–Gothenburg rail line, making it the convenient interchange if you're arriving by train from elsewhere in Sweden.
By car: From Gothenburg, take the E20 east and then Route 44 north — about 120 km, under 90 minutes. From Stockholm, it's around 350 km via the E20. Driving is by far the most flexible option for reaching Läckö Castle and Kinnekulle, neither of which is easily accessible by public transport.
By air: The nearest airports are Gothenburg Landvetter (around 100 km south) and Stockholm Arlanda (around 400 km east). Neither is particularly convenient; most visitors travel by road from within Sweden.