There is no nonstop path linking Bush Intercontinental to the Latvian capital, which means booking business class from Houston to Riga is really an exercise in choosing the right European gateway. In practical terms, the answer to "what's the best way to fly business class from Houston to Riga" is a one-stop itinerary via Frankfurt or Munich on Lufthansa, or a two-stop routing through Amsterdam or Paris on Delta with airBaltic handling the final hop into RIX. Lufthansa's IAH-Frankfurt sector operates on the 747-8 or A380, and depending on aircraft assignment you may find yourself in the newer Allegris business suite with a closing door, though older long-haul configurations with the standard herringbone-adjacent seat still appear on this route, so it pays to check your specific aircraft before booking. From Frankfurt, the short connection down to Riga is typically flown on a narrowbody in a standard Euro-business setup — comfortable, but don't expect lie-flat seating on that final leg.
Having connected through Frankfurt and Munich multiple times on this exact itinerary, my strongest recommendation is to build in at least a 90-minute buffer at either hub during winter months, when de-icing delays are common and can cascade into missed connections onto the once- or twice-daily airBaltic flights to Riga. Munich's passport control for non-Schengen arrivals can also bottleneck badly in early morning banks, so Frankfurt is often the safer transfer point despite its size. If Delta's routing appeals to you, their transatlantic joint venture with Air France-KLM means you'll likely fly a Delta One suite with a closing door across the Atlantic, then connect onto a KLM or Air France regional jet into the Baltic — a solid option if your dates align better with their schedule.
Late spring through early autumn — May through September — brings the best combination of fare availability and pleasant Baltic weather for your Riga arrival, as airlines add capacity for the Nordic and Baltic tourism season. Because pricing on this three-airline, multi-hub route fluctuates constantly with fuel surcharges and seasonal demand shifts, setting up fare alerts is the smartest way to catch a premium-cabin deal before it disappears.