Your installed version is LR 6.14 (not Classic). 6.14 is the final version of standalone Lightroom, and will not receive any more updates.
LR Classic (version 7) is only available by subscription. The Photography Plan, which includes LR Classic, the new cloud-based LR CC and Photoshop is $10 a month.
Lightroom Classic CC is currently at version 7.1 [ 1148620 ] (Expecting Classic-CC v7.2 in near future)
Lightroom Classic CC is only available by subscription to the Photography Plan.
Lightroom 6.14 is the last and final version that can be purchased as "Stand-alone".
Is there a way to force my LR installation to update to the latest LR classic build 6.2 ?
No. There is no "LR classic build 6.2"
Lightroom Classic CC is "Desktop" based. It installs on the computer, it runs in the computer, the photos are stored in the computer.
The Photography Plan with Lightroom Classic and Photoshop is the best value by subscription. (US$9.99/month)
Edit: Doooooh I must be a slow typist
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Adobe LR revision version numbers go like this: 6.0, 6.1, 6.2 ........ 6.10 .... ending up with 6.14 which is the latest (and last) revision. The rev. numbers are not decimal values. Rev 6.14 is much later than 6.2