Laos Airlines?

The first Link...

You can book on the go once there, with a few days notice, unless its Xmas-New years...

Laoairlines.com is the official one (your second link).

Lao-airlines.com is a travel agency base in Paris.

Hacky has it right, the first link with the hyphen in the address is the french agent, not Lao Air. This agency has created look-alike websites for three local carriers in SouthEast Asia, the other two in Myanmar. There have been reported problems in the past with Lao Air honoring pre-paid bookings from this agent, don't know how it has been lately. We were not able to use the bookings we had half paid in advance through them, and had to buy new full fare tickets from the Lao Air office in Vientiane to make our flight up to LP. The french agent did eventually refund our prepaid fare, but it took a few months to sort out and was a hassle, I would not recommend using that site to book tix with Lao Air. If you need to book ahead from home, try finding a travel agent in your area to help you out, or call the Lao Air reservation office listed on the second site.

Sorry....

I meant the 2nd one...

Thanks everybody! :-)

After some hesitation, 2 months ago, I booked my LP-Chiang Mai ticket with www.laos-airlines, the French agent and it worked out fine. The website gives an overseas price which is $15 cheaper than the price in Laos, but see below.
I made the reservation on the website at the overseas price. Received an e-mail a day or two later with attached invoice for half the payment. $15 was added to price quoted on webiste for taxes, $1.50 credit card fee, and payment had to be made to Thai office, and as per Thai law, had to made in Baht. The conversion (using what I thought was slightly unfavourable rates - but overall it does not amout to much) in Baht was shown on the invoice.
And I had to fill in my credit card details on the invoice and fax it to the Thai office. Many people will be uncomfortable with this. I used a credit card with a maximum limit which is not too much (I use this credit card for precisely this type of payments) as a precaution.
Received a voucher as e-mail attachment a few days later which I was asked to print. The voucher gives details of flight, amount paid and amout due in USD at LP office.
In LP, I went to Lao airlines office, as requested, and told the lady at the counter that I have made a reservation on internet and have come to pay the remainder and collect my ticket, and gave her the voucher. She looked ta it and seemed to make a slight nod, entered some info on the computer and after a couple of minutes she gave an invoice to pay at the cashier's cubicle and afterwards she gave me my ticket. No problem whatsoever.
I was told to collect my ticket at least 24 hours before departure. If you are arriving at the town of your departure only a dya or two before, and the office in closed (like on Sunday), maybe there will be a problem, I am not sure.