should be easy enough to do yourself. 12 or 14 awg 2 conductor lamp cable, a male connector (edison, english, whatever) a new bulb socket if necesary. feed the cable through the lamp (a cable snake might help) and attach each wire to it's respective terminal on the bulb socket. The "hot" and "neutral" wires should be indicated in some way (black for hot, the letter L, etc., and white for neutral, the letter n, etc. ) as should the terminals on the bulb socket (possibly a brass screw for hot, and a silver one for neutral). But crossing them really won't make a difference. A ground is not necesary and most modern lamps don't even have it. If the lamp chassis is metal you could ground it to prevent it from becoming energized, just get a three conductor cable and solder or bolt the ground wire to the metal chassis in an inconspicus place.

take apart another old lamp(you might have to purchase or borrow one) note how it was assembled and put yours back together the same way.the only safety issues are crossing the wires and this is easily figured out once you have a good look at a working lamp. I've done it many times as I collect old lamps.

I would get them professionally done. If they are that old they are likely to have all sorts of safety hazards that would not apply to modern items, such as no earth, metal fittings etc. It would be extremely dangerous to try to do it yourself unless you were totally au fait with modern safety standards.