Depends which one you bought. There are 3 options to buying Pro. The Default one is for 6 months support & updates. Another is called Extended & gives 12 months of such. The 3rd one is a 'one' off buy which means you pay for just that download version, no updates, no chance to redownload it afaik. That's the cheaper version.

Check your email account. Find the email from customer support, check the link they gave you ... see if it is still active. If it is, then you are in luck. BOOKMARK that personal download page of yours. You can of course also send that email to yourself on the other computer to download pro. There is no restriction on how many computers you use pro on.

For your sake, I'm hoping you got the 6 month version.

Checking the pro page:

Get Pro for a single payment of only $21.95 for 6 months support.
Get PRO for 1 year for only $34.95!

hmm I cannot see the 'one off' offer any more, perhaps they removed it. I see a different one for LW Portable. The 'one off' version cost around $14 from memory.

Let us know which one you purchased.

Besides, 'if' you still have the pro installer, you can simply copy it across to the other computer.

BTW ... FYI ... check Upgrading to V 4.18 as this info you should be aware of. Some people get confused, which is why I highlighted it here.