People in the Bangkok area have same issue. There are some lychee varieties that do better in these climates. The following was pulled from an agricultural paper. We've had more than a few discussions concerning this topic, so you might want to do a search...ya might find some more info on this.
Lychee cultivars growing in Thailand can be divided into 2 groups based on their cool temperature requirements.
(i) Moderately low temperature cultivars: Cultivars in this group normally possess Thai names and are grown mainly in the lowland and the central area (including eastern and western regions). Adaptability of these cultivars to the local climate is probably the main season. More than 10 cultivars have been recorded but the most famous one is the ‘Kom’ (dwarf) cultivar due to its compact canopy size. Other cultivars of less importance are Kra-lok Bai-Yaw, Sampao Kaew, Sa-rack Tong, Jean, Jean Yak, Tai, Tai Yai, Chor Rakum, Kiew Waan, Dang Payom, Kratone Tong Pra-rong and Kra-lok Bai Dum. Recently, ‘Pantip’ lychee variety emerged and is grown mainly in Kanchanaburi province.
(ii) Low temperature cultivars: There are a few cultivars in this group which are grown mainly in the north. The lowest temperature requirement belongs to ‘Hong Huay’, which contributes more than two-thirds of the whole group. This is followed by Chakrapad, Kim Cheng, O-Hia and a few other less important cultivars. Chakrapad usually fetches the highest price due to its larger fruit size.