It happened at the Mill Street level crossing in Leominster, Herefordshire, at 05:50 GMT on Friday.
The nearby A44 is likely to be closed all day, Hereford and Worcester Fire and Rescue service said. Rail services between Hereford and Shrewsbury are expected to be disrupted for most of the day.
No-one was injured in the crash.
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A specialist firm was brought in to help move the lorry, which was left leaning at an angle against the house.
The house is damaged but inspections are still going on to see how bad the situation is, Martin Lown from Hereford & Worcester Fire and Rescue Service said.
"We've got a structural engineer on site and as the recovery continues we will monitor the situation," he said.
Replacement buses are running between Shrewsbury and Hereford.

Southern Railway luggage van No 2464 has spent four months being stripped and repainted at Locomotion, the National Railway Museum in Shildon.
The carriage transported Churchill's coffin from London to Oxfordshire in 1965.
Manager Gary Campbell, said the restoration was something a lot of people in the town were "proud of".
The newly restored carriage, which cost about Â£30,000, will now move to the National Railway Museum in York.
It will be joined by the locomotive which pulled it as part of an exhibition commemorating the 50th anniversary of the former Prime Minister's state funeral.
After the funeral in London, his coffin was loaded into the carriage which was then drawn by Battle of Britain locomotive Winston Churchill to Oxfordshire.
Thousands gathered along the route to pay their respects.
Churchill was laid to rest in the parish churchyard of Bladon, close to Blenheim Palace, where he was born 89 years earlier.
The carriage was built in 1931 and was used during World War Two on evacuation trains before being put into Pullman colours in the 1960s.
It was moved to Los Angeles in 1966 but returned to the UK in 2007 where it entered the Swanage Railway Collection.

Former Chilean Football Association president Harold Mayne-Nicholls, 56, was one of five senior officials Fifa said were being investigated.
Mayne-Nicholls has served the suspension because the initial seven-year ban was issued in 2015.
He admitted speaking to officials from Qatar's bid about work placements for relatives at the Aspire youth academy.
Fifa's ethics committee felt those conversations provided "cause enough to doubt the integrity of the inspection process", according to leaked emails between a committee member and Mayne-Nicholls.
The Chilean's ban was initially reduced on appeal to three years, but on Friday it was further cut to two by the Court of Arbitration for Sport.
Mayne-Nicholls chaired Fifa's bid evaluation group for the 2018 and 2022 World Cups, which were awarded to Russia and Qatar respectively.
In his 2010 report to Fifa, Mayne-Nicholls expressed serious concerns about conditions in Qatar, where summer temperatures can reach 50C.
Mayne-Nicholls was one of several senior Fifa officials to call for an independent report into the award process for the 2018 and 2022 World Cups to be published in full.
A lorry carrying 28 tonnes of grain has crashed into a house next to a level crossing.
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The carriage which carried Sir Winston Churchill's coffin to his final resting place has been restored.
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A Fifa official who assessed bids for the 2018 and 2022 World Cups has had his ban from football cut to two years.