No. For a start, it is a complete myth that anything called a 'truck' in the US will automatically be called a lorry in Britain. In fact, a lorry is a fairly specific vehicle : it's large (often articulated) commercial haulage vehicle for the long-distance transportation of goods/freight. If it doesn't do that, it isn't a lorry. In many cases, what an AmE speaker would call a truck would also be called a truck in Britain, or else something different entirely, such as a 'van'. As for the paving truck, I agree with Paul that 'paving lorry' is wrong. ( Unless, of course, it's a haulage vehicle transporting paving material from one part of the country to another). Paving truck or tarmac truck sound OK. Or else, paver or asphalt paver. (Just out of interest, I googled 'paving lorry', and got one hit. One. Out of the vastness of the internet, one story from the 'Arabian Post' website. I think that counts as not existing if you only get one source. Not including a redirection to this very page on italki!)

It sounds very awkward and I daresay that no, it is not used as a term. Paving truck sounds fine to me, or paver. Or asphalt paver. Or tarmac truck. But 'paving lorry', no.

Google doesn't return any examples of "paving lorry", so I think it's unlikely. But I have no experience of the construction industry. You might find it helpful to study the language in this article, which is from a British construction website: https://www.constructionenquirer.com/2014/02/12/block-paving-truck-knocks-down-doncaster-footbridge/ They use "paving truck" the first time it is mentioned, and "lorry" afterwards.