It is my observation that a Frenchman will do almost anything to avoid double objective pronouns - for fear of making mistakes and because they sound fussy, awkward, and a bit snobbish. As they are used less and less frequently, the "correct" order is being lost even to the French. I have been encouraged by my teachers to reformulate to avoid this mare's nest. So
Je lui ai donné cela plutôt que je le lui ai donné.
That's a very interesting comment! ;-)
If we look at the sentences you wrote, they don't really mean the same (in essence):
Je lui ai donné cela = I gave this to him
Je le lui ai donné = I gave it to him
Using direct and indirect object pronouns together is still very much used in written form as well as when speaking French. As a native French speaker, I (and members of my family) use them together (how frequently, I couldn't say) without thinking I am sounding posh or else ;-)
I hope this is helpful.
Bonne journée !
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