About watering, after reading several sites, in conclusion all of them say this:

When actively growing, it requires more frequent watering and should not be allowed to become completely dry. It should be kept on the dry side after flowering until it begins its new growth.

Laelia tenebrosa normally begins growing in the early autumn in the United States, and will complete its new growth by midwinter. It will then rest for several weeks and flower in late spring to early summer, depending on the clone.

Charles Baker says:

WATER: Rainfall is moderate to heavy most of the year with somewhat drier conditions for about 3 months in winter, but average rainfall may be somewhat greater in the higher elevation habitat. Cultivated plants should be watered heavily while actively growing, but the roots must always dry
rapidly after watering. Water should be reduced somewhat after new growths mature in autumn.

I believe there's some contradition between both texts about the growing period.
What's your experience?

I've had both L. purpurata and L. tenebrosa for a few years. They are growing on my lemon tree. I didn't include any moss when I attached them to the tree. Neither orchid has a problem with the amount of rain that we get during winter. During summer I water them two or three times at night.

And, in your case, when it's their growing season?

They grow when it's warm and rest when it's not.

So they the most rain when they rest. Am I right?
And how are your temps on the rainy season?

Here's the climate for Los Angeles. It rains here during winter... when it's cool/cold and the L. tenebrosa is resting. When it's summer/warm here and the orchid is growing, it doesn't rain. We have a Mediterranean climate.

There aren't any epiphytic orchids that are native to Mediterranean climates. The closest exception might be Polystachya ottoniana.

Even though epiphytic orchids aren't native to Mediterranean climates, I grow 100s of them outside year around. Most of them are mounted without any moss. I rarely lose any to the winter rain or occasional frost.

You and I both have Mediterranean climates but I haven't been able to easily compare them. I clicked on the link in your signature but the data is formatted differently than Wikipedia.

The stake would not move the plant. Rather, it would hold the plant in its current position. Better stability is always beneficial!

In avg, I have higher temps in summer and lower in winter, both by 2~3ºC (3~5 F). So, the avg amplitude here is 6ºC higher than LA (10 F). This is easily explained because I'm far from the coast line.
About rain, my dry season is shorter than yours.

In general our climates are similar but mine has a continental trend.

I've put near a south window and I hope the leaves move up. Thanks for the sugestion.

rbarata, are you interested in trading climates? I am. I would be happy with more cold if it also meant more rain.

How many of your orchids have been killed by the cold?

Thinking about orchid growing I would be happy to live is a climate like yours but I have a sick enjoyment of the high temps in summer, which I love.

So far none of my orchids were killed by cold but the only ones I have outside are cymbs.

But inside I have some rooms that get temps around 12ºC (53 F) in winter. That's where I grow my cool growers. They are also the coolest in summer.