Dean Morgan and Chris Coyne had shots cleared early on as Luton began well before Leeds took charge.
Douglas' right-foot shot broke the deadlock just after half-time, before Lewis bundled in Rob Hulse's cross.
Luton responded and pulled one back through Steve Howard but Sol Davis' late dismissal ended their chances.
Luton boss Mike Newell:
"Everywhere we go, we create chances and play good football - but we are not getting results.
"It is becoming more than frustrating, but I am still pleased with the way that we played.
"We were done by a five-minute spell in the second-half, but apart from that there wasn't a lot to worry us."
Leeds: Sullivan, Kelly, Butler, Gregan, Crainey, Blake (Moore 87), Miller, Douglas, Lewis, Hulse, Healy (Bakke 70).
Subs Not Used: Bennett, Einarsson, Griffiths.
Booked: Hulse, Douglas.
Goals: Douglas 49, Lewis 53.
Luton: Beresford, Edwards, Barnett, Coyne, Davis, Brkovic (Feeney 63), Foley, Morgan (Showunmi 63), Underwood, Vine, Howard.
Subs Not Used: Perrett, Holmes, Brill.
Sent Off: Davis (90).
Booked: Davis.
Goals: Howard 83.
Att: 23,644
Ref: K Hill (Hertfordshire).