First, dump all those empty statements (; followed immediately by newline).

It might be better to swap the order of arguments, so the optional one is last:

file=$1
path=$(realpath -es "${2:-$PWD}") || return 1

(No need for quotes for RHS of assignment; explicit fail instead of depending on set -e).

The conditional printing gives an error return when $SH_DEBUG is unset; turn it around so that the pipeline is always true. Expand as ${SH_DEBUG-} so that this works when set -u -e. Log output should go to standard error stream, not output.

Since we have an absolute path and we're not expanding symlinks, we can use a simple pattern substitution in the iteration, rather than :

path=${path%/*}

We could turn the loop around, so that it terminates when the file is found, instead of repeating the test.

Modified code

#!/bin/sh

set -eu  # will work with any combination of these flags

lsup() {
    file=${1:-}
    [ "$file" ] || return 1
    path=$(realpath -es "${2:-$PWD}") || return 1

    [ -z "${SH_DEBUG-}" ] || echo >&2 "Searching for ${file} from ${path}…"

    until [ -e "${path}/${file}" ]
    do
        [ -z "${SH_DEBUG-}" ] || echo >&2 "Not found in ${path}/"
        [ -n "$path" ] || return 1
        path=${path%/*}
    done
    echo "${path}/${file}"
}