Trip from Alaya Resort Ubud to Lempuyang Temple is approximately 62.5 km and takes 2 hours. You can hire a transport with driver service which can be found in central area of Ubud or on Internet.
In general, the private transport service from Ubud to Lempuyang Temple costs around IDR 500.000 to IDR 1.400.000 (depends on type of car, trip time, and amount of participant).
As an alternative, you can also take a tour with a tour operator in Bali. Its cost is around IDR 750.000 (depends on facilities and number of destinations).
By most of operators, tour to Lempuyang Temple usually has a duration of 8 hours (full day) and is combined with others spots in East Bali namely: Tirta Gangga Water Palace, Taman Ujung Water Palace, Tukad Cepung Waterfall, and Amed Beach.
You may choose one of service options above to help you in getting Lempuyang Temple from Alaya Resort Ubud.