The lodge you want is St Thomas of Aberbrothock, no 40. That is an old spelling of Arbroath. It is a town on the east coast of Scotland near Dundee. No 40 is the oldest of the three lodges there, it dates from 1740. Their address is The Masonic Hall, West Newgate Street, Arbroath, Angus, Scotland.
To see if they have their own site check
WWW.grandlodgescotland.com. It lists the lodges by province. For them Arbroath is part of Forfarshire.
I am sure if you send a copy of your ancestors photo with your request the lodge would be glad to have it. Also they might be able to find him in any others they have of the period which do not have the names of the office bearers and brethren in it marked on them.
Do let me know how you get on and if there is anything else I can find out for you.