Remember new roots come almost exclusively from new growth. Old roots in the pot aren't very important, and old growths won't last many more years. Many people do what Roberta suggested and just drop an old pot into a new one.
If you don't want to look at the old pot, cut off the bottom and set it into the new container. Back-fill with new medium.
Maybe a nearby tavern or restaurant could save wine corks for you? I hear they are good medium for Laelias.
Done!
Had to improvise 'cause I haven't enough medium size bark. So I put a layer of flat river stones on the bottom, followed by a layer of leca, then a layer of large bark and, finally, the main layer of medium size bark+leca+cork chips.
I needed to raise the plastic pot because the rhizome is not only growing out of the pot but is growing down too.
I'll find a way to stabilize better the plastic pot using flexible garden wire.
Looks good! Now, just let it enjoy the fresh air outside. From the leaf color, more light will be beneficial - and this is a good time to start increasing light, before the summer sun arrives. At this time of year, it should have be able to acclimate naturally.
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"Extraordinary claims require extraordinary evidence" Carl Sagan
How would you water it, Roberta?
Would you pour water in and in the vicinity of the plastic pot or the complete clay pot?
It's in full sun most of the day but I'm not sure if it will dry that fast.
Day temps are oscillating between 28 and 22 ºC (82~70 F) but by night they drop to 12ºC (53 F).
I would water the whole thing. How often? You will have to see how fast it dries. Your temperatures are still rather cool (actually, nearly identical to mine). I think with the rather small amount of bark that you have in there, it will dry quite fast, especially if the sun is bright and the humidity is not high. I would guess that every 2-3 days for water would be OK, increase frequency as day length and sun intensity increase. Once you get to summer, you could water this every day and it would be happy because I expect that it will dry quickly.
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"Extraordinary claims require extraordinary evidence" Carl Sagan