I'm in a similar boat to you (3 kids, 2 whom are still in boosters). I was looking for a 2011 with <60k miles for around $40k-42k. I ended up buying a CPO 2013 with 48k for $49,000. The price on the LXs converges with the LC after 5-6 years. I considered the LX because the air suspension would be better for towing, but in the end decided I preferred the Toyota badge. Also the 2013's have all the same bells and whistles as the 2011 LX.
As far as price goes, for $30k you'll be looking at a 2008-2009 with at least 90k on it, possibly more. I spent a lot of time looking nationally on cars.com, cruising ebay, etc. Since the LC is low production, what I found was that you'll need to make one of the following trade-offs:
- You'll have to travel somewhere to make the purchase or will need to have the vehicle shipped, or
- You'll need to adjust your criteria (cost, mileage, accident history, etc), or
- You'll need to have a very long purchase timeframe (6+ months) to wait for your mileage/condition/price to turn up locally
In the end I decided a 2013 CPO was the way to go as would let me take a little longer loan since we only drive 9-10k miles per year. I had mine shipped by AutoNation from Houston to Chicago (it's actually slated for delivery on Monday). Normally buying sight unseen would concern me, but it was 2 years old, had a clear carfax, and I was able to get all the service records from one dealership. With the Toyota CPO warranty I feel covered for any issues.
One thing I do suggest is that you go buy three car seats and try to put them in the vehicle now. We managed two car seats and a booster and then two boosters and a car seat in our Acura MDX just fine, but three across wouldn't have fit. I know the LC has a bit more room in the 3rd row, but 3 seats all facing the same direction might be tough. If they don't fit, you can try to find a slimmer car seat, but I would caution in your case about relying on the 3rd row since in my experience with my Acura the 3rd row is a PITA to get kids in and out of if they can't buckle themselves (plus once you fasten the car seat, you can only access the 3rd row via the trunk).