In calling all men to "lift holy hands," Paul is simply encouraging people to pray as they always have, albeit in a more pure manner.
The Hebrews (and later the Jews) prayed in all sorts of postures (i.e. lifted hands, lifted eyes, heads down, on knees, heads bowed, prostate.) as can be seen in the old testament.
However the green word used here, translated 'men', means "males" opposed to all mankind. Probably referring to only the men who were leading in prayer in the meeting places in which Timothy was an overseer. Paul was instructing him in how instruct those he was in charge of overseeing - to see to it that they had "clean hands" before praying as can be seen in the previous chapter.
But the goal of our instruction is love from a pure heart and a good conscience and a sincere faith.
-- 1 Timothy 1:5 (NASB)
It was an ancient custom but Paul was not giving Timothy instructions to Timothy or anyone else to "lift holy hands". Nor was it ever a command. He was simply telling them to instruct his men leaders to ensure their "hand were clean" (spiritually speaking) before offering prayers.
We also see this elsewhere where we are instructed before making an offering at the altar (prayer). If we remember we have ought against someone - some unfinished business of reconciliation - we should "leave our gift" and go be reconciled first. Paul also later instructs Timothy to ensure leaders are "blameless".
This is the principle being taught. It is not about lifting hands any more than we are to greet each other with a holy kiss. :)