“Lo siento por tu perdida” is “I’m sorry for your loss.”
It’s prononuced Low see-En-toe pour two pair-DEE-da
The only thing I’m not sure about is if you should be using “tu” which is the familiar “you”. I think now it is almost always used rather than the formal (Some countries use vos, Guatemala apparently does some, but I’m sure they’d know tu as well.) That is also the singular form for speaking to one person “Vosotros” is the plural familiar you, but I think most of South America uses Ustedes.
You didn’t really avoid the tú/usted issue since you used “su” (which can go with “usted” or “ustedes”). It would not be clear from that phrase whether you were saying “I lament your [family’s] loss” or “I lament your [personal] loss”, with the latter being the formal phrasing (as opposed to “Lamento much tu perdida”, the informal phrasing).
But I think you’re right about that phrasing. As a gringo, it’s best to err on the formal side.
Thanks all. I stuck with “lo siento.” Luckily a bilingual person (grandson) was nearby for some translations. It was more a matter of showing up, of course, than anything I might eloquently say in any language.