How can you even start guessing what language your Lechites spoke?!
Lechites did not exist.
It is a term coined later to describe North-Western Slavs, descendants of legendary Lech (or Lechius in Latin).
There was a legend about two brothers - Lechius and Czechius. Another version has three brothers - Lech, Czech and Rus.
According to this legend Czechs, Slovaks and Lusatians / Sorbs are descendants of Czechius (Czech).
Poles ("Lachs" is the name for Poles in East Slavic), Pomeranians, Polabians* are descendants of his brother - Lechius (Lech).
*Polabians consisted of Obodrites, Veleti and Rujani.
And Russians, Belarusians, Ukrainians according to this legend are descendants of third brother - Rus.
Modern linguists figured out that there is indeed a division for Northern and Southern branches among West Slavic languages. Czech-Slovak-Sorbian languages are the South-Western branch; while Polish-Pomeranian-Polabian languages are the North-Western branch.
Therefore they called these North-Western Slavic languages - Lechitic languages - after that legendary guy called Lech.
http://en.wikipedia.org/wiki/Lechitic_languages
The South-Western Slavic group was called "Czecho-Slovak languages". And Lechites = North-Western Slavs.
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In East Slavic languages the name for Poles is "Lachs" or "Lyakhs" and similar.
Poland is (or was in the past) "Lechistan" in Turkish language. "Lechia" was also a name for Poland.
Probably the legend is very old and these names are derived from that legend.
In the Middle Ages and in the Early Modern Era Poles were frequently called "Sarmatians", "Vandals", "Scythians", etc.
So this is nothing strange. People derive names from legends or from ancient inhabitants of the same territory.
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White Croats were Slavs - all Croats are Slavs, and their name is no more "Iranic" than that of Serbs or Czechs. After all, people called Serboi are mentioned for example by Pliny the Elder (23 - 79 AD), as a tribe living in the region of Caucasus. There was an ancient Scytho-Sarmatian tribe called Zinchi / Cissi. It is a similar story as with Horohoati / Chroates, who are placed by Persian and Greek Hellenistic sources in Arakhosia (region called Harahvati in the Avestan language). Later there was also a tribe called Choruatos - mentioned as living near Caucasus and near eastern banks of the Black Sea. But as I wrote - we could as well claim that Serbs are descendants of Pliny's Serboi and Czechs are descendants of ancient Zinchi / Cissi. There are alternative, Non-Iranic, Slavic etymologies for all these names too.