If I had won the lottery i would have bought a new house -
Gdybym byl wygral na loterii, kupilbym nowy dom.
No. 'byl wygral' is disappearing from our language as a marker of the 3rd conditional and there can be no difference between the verb endings used in 2nd and 3rd cond. sentences (I am using the English terminology, because this lack of difference means that these conditionals do not exist as separate entities in Polish). I think that people will usually add a phrase that refers to past time to make sure they are referring to the past.
"Gdybym WTEDY wygral na loterii...."
or
"gdybym wygral na TAMTEJ loterii" ('that lottery')
However, I liked the use of 'bylbym" in the second part of the sentence
kupilbym OR bylbym kupil nowy dom
Sometimes it is used as a kind of incoplete conditional:
bylbym go zlapal (I would have caught him = I nearly caught him)
bylbym zadzwonil (I would have called = I was going to call you, but...)
In the second conditional only "kupilbym" can be used.
"kupie" is a straightforward future reference. It is used in 1st condtional sentences, where "gdyby" is not possible
"Jesli wygram na loterii, kupie nowy dom"
'bede kupowal' makes little sense to me in this context.
Now
"Gdybym wygral na loterii, kupie nowy dom" mixes the first and second conditionals, but doesn't sound appallingly ungrammatical to me. I wouldn't correct it as readily as "If I won... I will buy". But then I'm not a native speaker of English....