Lines whitewashed seven-time world champion Hendry 3-0 in the semi-finals before beating John Parrott 4-0 in the final.
Lines, whose son Oliver is also a professional player, will now feature in the World Championships qualifying at Ponds Forge next month where he will be looking to seal his place in the first round for the first time since 1998.
Coincidentally, the Leeds cueman's last appearance at the Crucible was ended in a 10-4 defeat by Parrott in the first round.
Hendry,48, had been attempting to reach the World Championships for a first time since he retired after being knocked out of the event by Stephen Maguire.
And although Hendry won his opening match on Thursday, the Scot was well beaten by Lines, a 47-year-old amateur who remains active on the main tour and beat the defending champion Neil Robertson at the UK Championship in November.
Hendry said: "I didn't play well. It feels like somebody else's arm out there.
"Peter played very solid and he deserves to be in the final. You need to be a bit sharper to compete."