The tower was the brainchild of St Martin's former rector, Lionel Webber, who went ahead with it before funding was in place. The project had a total cost of £660,000.
A hearing at the High Court in June, instigated by Mowlem, heard that the Webber had issued Mowlem with six or seven cheques over an 18-month period, but none had been honoured.
A spokesperson for the contractor said: "We are still working with the church council. I suspect this [the bid for lottery money] is part of their attempt to raise funds."
A commission spokesperson confirmed that the church had made a bid for lottery funds.
Work on the tower came to a halt two years ago when it became apparent that the church could not pay the contractor and it has been cordoned off ever since.