USCIS has announced that, effective February 19, 2019, it is partially resuming 15 day premium processing of all categories of H-1b petitions, but only for those filed prior to December 22, 2018. USCIS had suspended most 15 day premium processing in September 2018, ostensibly to catch up on backlogged cases and to "[b]e responsive to petitions with time-sensitive start dates" (which no doubt would have benefited greatly from the just-suspended premium processing option).
Employers with pending H-1b petitions filed on or before December 21, 2018, on the basis of changed employer, change of job duties, or new worksite location, may now request 15 day processing of those petitions by filing a premium upgrade request and paying the $1410 filing fee.
USCIS made no commitment as to when it will resume premium processing H-1b petitions filed after December 21, 2018, saying only that it will do so "as agency workloads permit".
Based on past practice, it is extremely unlikely that USCIS will permit premium processing of FY2020 H-1b petitions to be filed in the April 2019 lotteries.
The September 2018 premium processing suspension notice had exempted two categories of H-1b petitions: 1) extensions of stay where there is no change to a prior approved petition; and 2) H-1b petitions filed by cap exempt employers such as universities and non-profit research institutions. These exemptions remain in effect, and USCIS will continue to accept premium processing requests with newly filed petitions in these situations.