//$cateinstance is the instance of MagentoCatalogModelCategoryFactory
$collection = $cateinstance->create()->load($cateid)->getProductCollection()->addAttributeToSelect('*')

$collection->addAttributeToSort('price', 'ASC');

$collection
    ->setPageSize(1) // only get 10 products
    ->setCurPage(1);

$lowest_price_product = $collection->getFirstItem();