the key word ARG has a different scope before and after the FROM instruction
Try using ARG twice in your Dockerfile, and/or you can try the ENV variables
ARG LANDING_PAGE_DOMAIN
FROM nginx:alpine
COPY nginx.conf /etc/nginx/nginx.conf
COPY production/* /etc/nginx/conf.d/
ARG LANDING_PAGE_DOMAIN
ENV LANDING_PAGE_DOMAIN=${LANDING_PAGE_DOMAIN}
RUN sed -i s/{LANDING_PAGE_DOMAIN}/${LANDING_PAGE_DOMAIN}/g /etc/nginx/conf.d/landing.conf
EXPOSE 80 443