I continued reading the newspaper and came across the anecdote in which лже Семён was mentioned. Unfortunately I could not find a rule which mentiones when to use псевдо and where to use лже. Is there a pattern or could they simply be used randomly? Thank you in advance!
лже is for impersonation (of, say, Tzar) or mimicry (of edible mushroom).
псевдо is for copying form without reproducing essense. Don't think it ever applies to animate being.
квази is sometimes used, meaning "unrelated, but essentially the same"
псевдо is greek and
лже is slavic; when making complex words, use together roots of same origin:
ложноножка, она же
Лже- in most cases expresses negative attitude (or strong denial of the sense the root of the word usually carries) while псевдо- is rather skeptical and often even neutral, especially when used in engineering and scientific terms where it means 'similar to smth. but strictly speaking, not exactly that thing'. Лженаука (much stronger than псевдонаука which is possible for expression of skepticism towards some theory), лжепророк, but (neutral) псевдоним, псевдостерео, псевдофланец, псевдокогерентный, псевдо-ЭВМ, псевдоуплотнитель and many more such words.