Thai and Lao are prime areas of exploration for the interface of lexical and post-lexical tone phonology. There does seem to be a lack of tone sandhi in the same way that many varieties of Chinese, such as Standard Mandarin or mainstream Xiamen (Amoy) & Taiwanese Hokkien / Southern Min have.
But Lao does have some interesting features in its synchronic post-lexical tone phonology. One 1994 overview on Vientiane Lao from 上田玲子 (Reiko Ueda), under section 4.3.6., states:
しかし,1の場合も,複音節語や文中にある場合は,全昇調[24]ではなく,低昇調[23]あるいは低平調[22]となる.つまり,低昇調[23]であることが多いか少ないかというちがいだけということになる.
(my very rough translation):
However, even in the case of {tone} 1, if it is in a compound syllable word or in a sentence, it will be a low rising tone [23] or a low level tone [22] instead of a low rising tone [24]. In other words, the only difference is whether the low rising tone [23] rises a lot or a little.
The example cited is ຫຼັງຄາ rangkha, "roof" (Japanese: 屋根), transcribed as /laŋ22kʰaː34/ , which is made up of ຫຼັງ rang "back" (Japanese: 後ろ), with tone [24], and ຄາ kha "foot" (Japanese: 足), tone [24] too.