[Grammar] lest+should & that+might. What's the difference?

[IDONTKNOWENGLISH]

Here are three sentences:
1) He had changed his voice lest it should be recognized.
2) He had changed his voice in order that it mightn't be recognized.
3) He had changed his voice so that it mightn't be recognized.

What construction should I use? lest+should or in order that+ may/shall or so that+can/will/may. and Is there any difference between them?

[bhaisahab]

Originally Posted by IDONTKNOWENGLISH

Here are three sentences:
1) He had changed his voice lest it should be recognized.
2) He had changed his voice in order that it mightn't be recognized.
3) He had changed his voice so that it mightn't be recognized.

What construction should I use? lest+should or in order that+ may/shall or so that+can/will/may. and Is there any difference between them?

All your three examples mean the same. The rest of your question is more complex, can you give some examples of how you want to use "so that+can/will/may"?

[IDONTKNOWENGLISH]

1) I have given him the key so that he can get into the house whenever he likes.
2)She will hide the presents so that the children will not find them
3)He is going to buy new furniture, so that she may be even happier in her new home.
I meen that what's the best way to say in speech? I've never heard lest+should? Won't it be wierd to say that in conversation?

[bhaisahab]

Originally Posted by IDONTKNOWENGLISH

1) I have given him the key so that he can get into the house whenever he likes.
2)She will hide the presents so that the children will not find them
3)He is going to buy new furniture, so that she may be even happier in her new home.
I meen that what's the best way to say in speech? I've never heard lest+should? Won't it be wierd to say that in conversation?

All your examples are correct. "Lest it should" is old fashioned and rarely used in modern English, whether spoken or written.