Dave at eevblog posted an excellent video series on designing custom LCDs, so I watched those a number of times.  I also found another eevblog user who posted a great writeup of a replacement LCD he designed for his Tandy/Radio Shack TRS-80 PC-1 (coincidentally I desperately wanted one of these when I was a kid).

The Fluke 8060a manual has a pretty good image of the display... it's not exactly the same as what you see on the glass, but it would have been close enough to use for a replacement.  However, I didn't feel quite right copying the work done in the manual, and I wanted to make a few of my own tweaks anyway so I created my own graphics for the LCD.  

I used Inkscape to draw the segments how I wanted them... I increased the digit size a tiny bit and also dropped the continuity bar down a little bit from the top of the display so I'd be able to see it better.  (with the original display I sometimes struggled to see if the continuity bar was ON, since it wsa so close to the display bezel which often cast a shadow on the top of the LCD)

The LCD details are:

1. Display Type - TN/Positive
2. Polarizer Type - Reflective
3. Drive Mode - 1/2 Bias, 1/2 Duty
4. Operating Voltage - 3V
5. Viewing Direction - 6 o'clock
6. Connector Type - Elastomer

The 8060 display pinout is:

pin  H1    H2
---------------
1    H1
2    cont  bar
3    rel   audible
4    A0    B0
5    G0    C0
6    E0    D0
7    F0    DP0
8    A1    B1
9    G1    C1
10   E1    D1
11   F1    DP1
12   A2    B2
13   G2    C2
14   E2    D2
15   F2    DP2
16   A3    B3
17   G3    C3
18   E3    D3
19   F3    DP3
20   1/2   1/2
21   BT    NEG
22   K     HZ
23         H2

The Inkscape image, the LCD details and the pinout then went into a document that I could send off to an LCD fabricator for a quote.