A great advantage of pewter is that it actually needs very little looking after. Your first thought of pewter might of that dull grey metal tankard - older pewter like this was shiny when new, but had a high lead content which made it go dull over time. Modern pewter doesn't contain lead and so will retain its shininess; it won't go as dull, however long you leave it. It will simply develop a subtle patina over time (we’re talking years here).
All you need to do to clean your Lancaster and Gibbings piece is use a soft cloth and a household furniture polish - and if it’s a photo frame, just use glass cleaner when you clean the glass.
I wouldn't recommend cleaning the pewter with silver polish; that will turn up the contrast on the piece to maximum, making the highlights too bright and the recessed areas too dark.
If you’ve left it a bit too long (or you need to remove the silver polish) washing in hot soapy water is good, but just getting a bit more vigorous with the cloth should also work.
How you choose to look after your piece will, to a slight extent, determine how it looks over time.
A lot of modern pewter has been dipped in acid to age it, to give it a patina, and then brushed to bring out the highlights. It’s a nice look, and can bring out the detail in a design very effectively, but it is like buying pre-washed jeans - it is what most people do, and it does look good; but it will never be as good as something that has aged with you over time.